Example 1: Factorize the quadratic expression: x^{2} -8x -9

Let's rewrite this expression as: x^{2} -8x -9

The middle term needs to be split into two terms whose product is -9x^{2} while the sum remains -8x

x^{2 }- 9x + 1x -9

= x(x - 9) + 1 (x - 9)

= (x - 9) (x + 1)

### Example 2: Factorize the quadratic expression: x^{2} +13x -168

Let's rewrite this expression as: x^{2} +13x -168

The middle term needs to be split into two terms whose product is -168x^{2} while the sum remains +13x

x^{2 }+ 21x - 8x -168

= x(x + 21) - 8 (x + 21)

= (x + 21) (x - 8)

### Example 3: Factorize the quadratic expression: x^{2} +3x -40

Let's rewrite this expression as: x^{2} +3x -40

The middle term needs to be split into two terms whose product is -40x^{2} while the sum remains +3x

x^{2 }+ 8x - 5x -40

= x(x + 8) - 5 (x + 8)

= (x + 8) (x - 5)

### Example 4: Factorize the quadratic expression: x^{2} +5x -300

Let's rewrite this expression as: x^{2} +5x -300

The middle term needs to be split into two terms whose product is -300x^{2} while the sum remains +5x

x^{2 }- 15x + 20x -300

= x(x - 15) + 20 (x - 15)

= (x - 15) (x + 20)

### Example 5: Factorize the quadratic expression: x^{2} +32x +240

Let's rewrite this expression as: x^{2} +32x +240

The middle term needs to be split into two terms whose product is +240x^{2} while the sum remains +32x

x^{2 }+ 20x + 12x +240

= x(x + 20) + 12 (x + 20)

= (x + 20) (x + 12)

### Example 6: Factorize the quadratic expression: x^{2} -15x -216

Let's rewrite this expression as: x^{2} -15x -216

The middle term needs to be split into two terms whose product is -216x^{2} while the sum remains -15x

x^{2 }- 24x + 9x -216

= x(x - 24) + 9 (x - 24)

= (x - 24) (x + 9)

### Example 7: Factorize the quadratic expression: x^{2} -39x +380

Let's rewrite this expression as: x^{2} -39x +380

The middle term needs to be split into two terms whose product is +380x^{2} while the sum remains -39x

x^{2 }- 20x - 19x +380

= x(x - 20) - 19 (x - 20)

= (x - 20) (x - 19)

### Example 8: Factorize the quadratic expression: x^{2} +22x +85

Let's rewrite this expression as: x^{2} +22x +85

The middle term needs to be split into two terms whose product is +85x^{2} while the sum remains +22x

x^{2 }+ 5x + 17x +85

= x(x + 5) + 17 (x + 5)

= (x + 5) (x + 17)

### Example 9: Factorize the quadratic expression: x^{2} -13x -230

Let's rewrite this expression as: x^{2} -13x -230

The middle term needs to be split into two terms whose product is -230x^{2} while the sum remains -13x

x^{2 }- 23x + 10x -230

= x(x - 23) + 10 (x - 23)

= (x - 23) (x + 10)

### Example 10: Factorize the quadratic expression: x^{2} -15x -76

Let's rewrite this expression as: x^{2} -15x -76

The middle term needs to be split into two terms whose product is -76x^{2} while the sum remains -15x

x^{2 }- 19x + 4x -76

= x(x - 19) + 4 (x - 19)

= (x - 19) (x + 4)

### Example 11: Factorize the quadratic expression: x^{2} -17x +16

Let's rewrite this expression as: x^{2} -17x +16

The middle term needs to be split into two terms whose product is +16x^{2} while the sum remains -17x

x^{2 }- 16x - 1x +16

= x(x - 16) - 1 (x - 16)

= (x - 16) (x - 1)

### Example 12: Factorize the quadratic expression: x^{2} -21x +90

Let's rewrite this expression as: x^{2} -21x +90

The middle term needs to be split into two terms whose product is +90x^{2} while the sum remains -21x

x^{2 }- 15x - 6x +90

= x(x - 15) - 6 (x - 15)

= (x - 15) (x - 6)

### Example 13: Factorize the quadratic expression: x^{2} -7x -170

Let's rewrite this expression as: x^{2} -7x -170

The middle term needs to be split into two terms whose product is -170x^{2} while the sum remains -7x

x^{2 }+ 10x - 17x -170

= x(x + 10) - 17 (x + 10)

= (x + 10) (x - 17)

### Example 14: Factorize the quadratic expression: x^{2} +7x -78

Let's rewrite this expression as: x^{2} +7x -78

The middle term needs to be split into two terms whose product is -78x^{2} while the sum remains +7x

x^{2 }+ 13x - 6x -78

= x(x + 13) - 6 (x + 13)

= (x + 13) (x - 6)

### Example 15: Factorize the quadratic expression: x^{2} -44x +483

Let's rewrite this expression as: x^{2} -44x +483

The middle term needs to be split into two terms whose product is +483x^{2} while the sum remains -44x

x^{2 }- 21x - 23x +483

= x(x - 21) - 23 (x - 21)

= (x - 21) (x - 23)

### Example 16: Factorize the quadratic expression: x^{2} -6x -247

Let's rewrite this expression as: x^{2} -6x -247

The middle term needs to be split into two terms whose product is -247x^{2} while the sum remains -6x

x^{2 }- 19x + 13x -247

= x(x - 19) + 13 (x - 19)

= (x - 19) (x + 13)

### Example 17: Factorize the quadratic expression: x^{2} -14x -32

Let's rewrite this expression as: x^{2} -14x -32

The middle term needs to be split into two terms whose product is -32x^{2} while the sum remains -14x

x^{2 }+ 2x - 16x -32

= x(x + 2) - 16 (x + 2)

= (x + 2) (x - 16)

### Example 18: Factorize the quadratic expression: x^{2} -8x -384

Let's rewrite this expression as: x^{2} -8x -384

The middle term needs to be split into two terms whose product is -384x^{2} while the sum remains -8x

x^{2 }+ 16x - 24x -384

= x(x + 16) - 24 (x + 16)

= (x + 16) (x - 24)

### Example 19: Factorize the quadratic expression: x^{2} -10x -119

Let's rewrite this expression as: x^{2} -10x -119

The middle term needs to be split into two terms whose product is -119x^{2} while the sum remains -10x

x^{2 }+ 7x - 17x -119

= x(x + 7) - 17 (x + 7)

= (x + 7) (x - 17)

### Example 20: Factorize the quadratic expression: x^{2} -9x -10

Let's rewrite this expression as: x^{2} -9x -10

The middle term needs to be split into two terms whose product is -10x^{2} while the sum remains -9x

x^{2 }+ 1x - 10x -10

= x(x + 1) - 10 (x + 1)

= (x + 1) (x - 10)

### Example 21: Factorize the quadratic expression: x^{2} -25x +66

Let's rewrite this expression as: x^{2} -25x +66

The middle term needs to be split into two terms whose product is +66x^{2} while the sum remains -25x

x^{2 }- 22x - 3x +66

= x(x - 22) - 3 (x - 22)

= (x - 22) (x - 3)

### Example 22: Factorize the quadratic expression: x^{2} +27x +140

Let's rewrite this expression as: x^{2} +27x +140

The middle term needs to be split into two terms whose product is +140x^{2} while the sum remains +27x

x^{2 }+ 7x + 20x +140

= x(x + 7) + 20 (x + 7)

= (x + 7) (x + 20)

### Example 23: Factorize the quadratic expression: x^{2} -6x -72

Let's rewrite this expression as: x^{2} -6x -72

The middle term needs to be split into two terms whose product is -72x^{2} while the sum remains -6x

x^{2 }+ 6x - 12x -72

= x(x + 6) - 12 (x + 6)

= (x + 6) (x - 12)

### Example 24: Factorize the quadratic expression: x^{2} -7x -30

Let's rewrite this expression as: x^{2} -7x -30

The middle term needs to be split into two terms whose product is -30x^{2} while the sum remains -7x

x^{2 }- 10x + 3x -30

= x(x - 10) + 3 (x - 10)

= (x - 10) (x + 3)

### Example 25: Factorize the quadratic expression: x^{2} +13x -198

Let's rewrite this expression as: x^{2} +13x -198

The middle term needs to be split into two terms whose product is -198x^{2} while the sum remains +13x

x^{2 }+ 22x - 9x -198

= x(x + 22) - 9 (x + 22)

= (x + 22) (x - 9)

### Example 26: Factorize the quadratic expression: x^{2} +32x +252

Let's rewrite this expression as: x^{2} +32x +252

The middle term needs to be split into two terms whose product is +252x^{2} while the sum remains +32x

x^{2 }+ 18x + 14x +252

= x(x + 18) + 14 (x + 18)

= (x + 18) (x + 14)

### Example 27: Factorize the quadratic expression: x^{2} +17x -38

Let's rewrite this expression as: x^{2} +17x -38

The middle term needs to be split into two terms whose product is -38x^{2} while the sum remains +17x

x^{2 }+ 19x - 2x -38

= x(x + 19) - 2 (x + 19)

= (x + 19) (x - 2)

### Example 28: Factorize the quadratic expression: x^{2} +2x -48

Let's rewrite this expression as: x^{2} +2x -48

The middle term needs to be split into two terms whose product is -48x^{2} while the sum remains +2x

x^{2 }- 6x + 8x -48

= x(x - 6) + 8 (x - 6)

= (x - 6) (x + 8)

### Example 29: Factorize the quadratic expression: x^{2} -20x -21

Let's rewrite this expression as: x^{2} -20x -21

The middle term needs to be split into two terms whose product is -21x^{2} while the sum remains -20x

x^{2 }- 21x + 1x -21

= x(x - 21) + 1 (x - 21)

= (x - 21) (x + 1)

### Example 30: Factorize the quadratic expression: x^{2} +28x +195

Let's rewrite this expression as: x^{2} +28x +195

The middle term needs to be split into two terms whose product is +195x^{2} while the sum remains +28x

x^{2 }+ 13x + 15x +195

= x(x + 13) + 15 (x + 13)

= (x + 13) (x + 15)

### Example 31: Factorize the quadratic expression: x^{2} -21x -22

Let's rewrite this expression as: x^{2} -21x -22

The middle term needs to be split into two terms whose product is -22x^{2} while the sum remains -21x

x^{2 }- 22x + 1x -22

= x(x - 22) + 1 (x - 22)

= (x - 22) (x + 1)

### Example 32: Factorize the quadratic expression: x^{2} +24x +63

Let's rewrite this expression as: x^{2} +24x +63

The middle term needs to be split into two terms whose product is +63x^{2} while the sum remains +24x

x^{2 }+ 3x + 21x +63

= x(x + 3) + 21 (x + 3)

= (x + 3) (x + 21)

### Example 33: Factorize the quadratic expression: x^{2} -10x -11

Let's rewrite this expression as: x^{2} -10x -11

The middle term needs to be split into two terms whose product is -11x^{2} while the sum remains -10x

x^{2 }+ 1x - 11x -11

= x(x + 1) - 11 (x + 1)

= (x + 1) (x - 11)

### Example 34: Factorize the quadratic expression: x^{2} -29x +204

Let's rewrite this expression as: x^{2} -29x +204

The middle term needs to be split into two terms whose product is +204x^{2} while the sum remains -29x

x^{2 }- 12x - 17x +204

= x(x - 12) - 17 (x - 12)

= (x - 12) (x - 17)

### Example 35: Factorize the quadratic expression: x^{2} -6x -391

Let's rewrite this expression as: x^{2} -6x -391

The middle term needs to be split into two terms whose product is -391x^{2} while the sum remains -6x

x^{2 }+ 17x - 23x -391

= x(x + 17) - 23 (x + 17)

= (x + 17) (x - 23)

### Example 36: Factorize the quadratic expression: x^{2} -28x +96

Let's rewrite this expression as: x^{2} -28x +96

The middle term needs to be split into two terms whose product is +96x^{2} while the sum remains -28x

x^{2 }- 24x - 4x +96

= x(x - 24) - 4 (x - 24)

= (x - 24) (x - 4)

### Example 37: Factorize the quadratic expression: x^{2} +20x +19

Let's rewrite this expression as: x^{2} +20x +19

The middle term needs to be split into two terms whose product is +19x^{2} while the sum remains +20x

x^{2 }+ 19x + 1x +19

= x(x + 19) + 1 (x + 19)

= (x + 19) (x + 1)

### Example 38: Factorize the quadratic expression: x^{2} -32x +240

Let's rewrite this expression as: x^{2} -32x +240

The middle term needs to be split into two terms whose product is +240x^{2} while the sum remains -32x

x^{2 }- 20x - 12x +240

= x(x - 20) - 12 (x - 20)

= (x - 20) (x - 12)

### Example 39: Factorize the quadratic expression: x^{2} +13x -30

Let's rewrite this expression as: x^{2} +13x -30

The middle term needs to be split into two terms whose product is -30x^{2} while the sum remains +13x

x^{2 }+ 15x - 2x -30

= x(x + 15) - 2 (x + 15)

= (x + 15) (x - 2)

### Example 40: Factorize the quadratic expression: x^{2} +3x -504

Let's rewrite this expression as: x^{2} +3x -504

The middle term needs to be split into two terms whose product is -504x^{2} while the sum remains +3x

x^{2 }- 21x + 24x -504

= x(x - 21) + 24 (x - 21)

= (x - 21) (x + 24)

### Example 41: Factorize the quadratic expression: x^{2} -11x -276

Let's rewrite this expression as: x^{2} -11x -276

The middle term needs to be split into two terms whose product is -276x^{2} while the sum remains -11x

x^{2 }+ 12x - 23x -276

= x(x + 12) - 23 (x + 12)

= (x + 12) (x - 23)

### Example 42: Factorize the quadratic expression: x^{2} +7x -18

Let's rewrite this expression as: x^{2} +7x -18

The middle term needs to be split into two terms whose product is -18x^{2} while the sum remains +7x

x^{2 }+ 9x - 2x -18

= x(x + 9) - 2 (x + 9)

= (x + 9) (x - 2)

### Example 43: Factorize the quadratic expression: x^{2} -29x +168

Let's rewrite this expression as: x^{2} -29x +168

The middle term needs to be split into two terms whose product is +168x^{2} while the sum remains -29x

x^{2 }- 21x - 8x +168

= x(x - 21) - 8 (x - 21)

= (x - 21) (x - 8)

### Example 44: Factorize the quadratic expression: x^{2} -22x +72

Let's rewrite this expression as: x^{2} -22x +72

The middle term needs to be split into two terms whose product is +72x^{2} while the sum remains -22x

x^{2 }- 4x - 18x +72

= x(x - 4) - 18 (x - 4)

= (x - 4) (x - 18)

### Example 45: Factorize the quadratic expression: x^{2} -9x +8

Let's rewrite this expression as: x^{2} -9x +8

The middle term needs to be split into two terms whose product is +8x^{2} while the sum remains -9x

x^{2 }- 8x - 1x +8

= x(x - 8) - 1 (x - 8)

= (x - 8) (x - 1)

### Example 46: Factorize the quadratic expression: x^{2} +4x +4

Let's rewrite this expression as: x^{2} +4x +4

The middle term needs to be split into two terms whose product is +4x^{2} while the sum remains +4x

x^{2 }+ 2x + 2x +4

= x(x + 2) + 2 (x + 2)

= (x + 2) (x + 2)

### Example 47: Factorize the quadratic expression: x^{2} -15x -216

Let's rewrite this expression as: x^{2} -15x -216

The middle term needs to be split into two terms whose product is -216x^{2} while the sum remains -15x

x^{2 }- 24x + 9x -216

= x(x - 24) + 9 (x - 24)

= (x - 24) (x + 9)

### Example 48: Factorize the quadratic expression: x^{2} +32x +240

Let's rewrite this expression as: x^{2} +32x +240

The middle term needs to be split into two terms whose product is +240x^{2} while the sum remains +32x

x^{2 }+ 20x + 12x +240

= x(x + 20) + 12 (x + 20)

= (x + 20) (x + 12)

### Example 49: Factorize the quadratic expression: x^{2} -20x +64

Let's rewrite this expression as: x^{2} -20x +64

The middle term needs to be split into two terms whose product is +64x^{2} while the sum remains -20x

x^{2 }- 4x - 16x +64

= x(x - 4) - 16 (x - 4)

= (x - 4) (x - 16)

### Example 50: Factorize the quadratic expression: x^{2} -49x +600

Let's rewrite this expression as: x^{2} -49x +600

The middle term needs to be split into two terms whose product is +600x^{2} while the sum remains -49x

x^{2 }- 24x - 25x +600

= x(x - 24) - 25 (x - 24)

= (x - 24) (x - 25)

### Example 51: Factorize the quadratic expression: x^{2} -12x -13

Let's rewrite this expression as: x^{2} -12x -13

The middle term needs to be split into two terms whose product is -13x^{2} while the sum remains -12x

x^{2 }- 13x + 1x -13

= x(x - 13) + 1 (x - 13)

= (x - 13) (x + 1)

### Example 52: Factorize the quadratic expression: x^{2} +23x +42

Let's rewrite this expression as: x^{2} +23x +42

The middle term needs to be split into two terms whose product is +42x^{2} while the sum remains +23x

x^{2 }+ 2x + 21x +42

= x(x + 2) + 21 (x + 2)

= (x + 2) (x + 21)

### Example 53: Factorize the quadratic expression: x^{2} +11x -42

Let's rewrite this expression as: x^{2} +11x -42

The middle term needs to be split into two terms whose product is -42x^{2} while the sum remains +11x

x^{2 }+ 14x - 3x -42

= x(x + 14) - 3 (x + 14)

= (x + 14) (x - 3)

### Example 54: Factorize the quadratic expression: x^{2} -23x +120

Let's rewrite this expression as: x^{2} -23x +120

The middle term needs to be split into two terms whose product is +120x^{2} while the sum remains -23x

x^{2 }- 15x - 8x +120

= x(x - 15) - 8 (x - 15)

= (x - 15) (x - 8)

### Example 55: Factorize the quadratic expression: x^{2} +16x +63

Let's rewrite this expression as: x^{2} +16x +63

The middle term needs to be split into two terms whose product is +63x^{2} while the sum remains +16x

x^{2 }+ 9x + 7x +63

= x(x + 9) + 7 (x + 9)

= (x + 9) (x + 7)

### Example 56: Factorize the quadratic expression: x^{2} +17x +60

Let's rewrite this expression as: x^{2} +17x +60

The middle term needs to be split into two terms whose product is +60x^{2} while the sum remains +17x

x^{2 }+ 5x + 12x +60

= x(x + 5) + 12 (x + 5)

= (x + 5) (x + 12)

### Example 57: Factorize the quadratic expression: x^{2} -27x +180

Let's rewrite this expression as: x^{2} -27x +180

The middle term needs to be split into two terms whose product is +180x^{2} while the sum remains -27x

x^{2 }- 12x - 15x +180

= x(x - 12) - 15 (x - 12)

= (x - 12) (x - 15)

### Example 58: Factorize the quadratic expression: x^{2} +17x +66

Let's rewrite this expression as: x^{2} +17x +66

The middle term needs to be split into two terms whose product is +66x^{2} while the sum remains +17x

x^{2 }+ 6x + 11x +66

= x(x + 6) + 11 (x + 6)

= (x + 6) (x + 11)

### Example 59: Factorize the quadratic expression: x^{2} -2x -3

Let's rewrite this expression as: x^{2} -2x -3

The middle term needs to be split into two terms whose product is -3x^{2} while the sum remains -2x

x^{2 }+ 1x - 3x -3

= x(x + 1) - 3 (x + 1)

= (x + 1) (x - 3)

### Example 60: Factorize the quadratic expression: x^{2} +10x -336

Let's rewrite this expression as: x^{2} +10x -336

The middle term needs to be split into two terms whose product is -336x^{2} while the sum remains +10x

x^{2 }+ 24x - 14x -336

= x(x + 24) - 14 (x + 24)

= (x + 24) (x - 14)

### Example 61: Factorize the quadratic expression: x^{2} -25x +114

Let's rewrite this expression as: x^{2} -25x +114

The middle term needs to be split into two terms whose product is +114x^{2} while the sum remains -25x

x^{2 }- 19x - 6x +114

= x(x - 19) - 6 (x - 19)

= (x - 19) (x - 6)

### Example 62: Factorize the quadratic expression: x^{2} +12x -189

Let's rewrite this expression as: x^{2} +12x -189

The middle term needs to be split into two terms whose product is -189x^{2} while the sum remains +12x

x^{2 }+ 21x - 9x -189

= x(x + 21) - 9 (x + 21)

= (x + 21) (x - 9)

### Example 63: Factorize the quadratic expression: x^{2} -8x -128

Let's rewrite this expression as: x^{2} -8x -128

The middle term needs to be split into two terms whose product is -128x^{2} while the sum remains -8x

x^{2 }+ 8x - 16x -128

= x(x + 8) - 16 (x + 8)

= (x + 8) (x - 16)

### Example 64: Factorize the quadratic expression: x^{2} -12x -325

Let's rewrite this expression as: x^{2} -12x -325

The middle term needs to be split into two terms whose product is -325x^{2} while the sum remains -12x

x^{2 }- 25x + 13x -325

= x(x - 25) + 13 (x - 25)

= (x - 25) (x + 13)

### Example 65: Factorize the quadratic expression: x^{2} +10x +9

Let's rewrite this expression as: x^{2} +10x +9

The middle term needs to be split into two terms whose product is +9x^{2} while the sum remains +10x

x^{2 }+ 9x + 1x +9

= x(x + 9) + 1 (x + 9)

= (x + 9) (x + 1)

### Example 66: Factorize the quadratic expression: x^{2} -3x -40

Let's rewrite this expression as: x^{2} -3x -40

The middle term needs to be split into two terms whose product is -40x^{2} while the sum remains -3x

x^{2 }- 8x + 5x -40

= x(x - 8) + 5 (x - 8)

= (x - 8) (x + 5)

### Example 67: Factorize the quadratic expression: x^{2} +40x +391

Let's rewrite this expression as: x^{2} +40x +391

The middle term needs to be split into two terms whose product is +391x^{2} while the sum remains +40x

x^{2 }+ 23x + 17x +391

= x(x + 23) + 17 (x + 23)

= (x + 23) (x + 17)

### Example 68: Factorize the quadratic expression: x^{2} -18x +45

Let's rewrite this expression as: x^{2} -18x +45

The middle term needs to be split into two terms whose product is +45x^{2} while the sum remains -18x

x^{2 }- 3x - 15x +45

= x(x - 3) - 15 (x - 3)

= (x - 3) (x - 15)

### Example 69: Factorize the quadratic expression: x^{2} +3x -238

Let's rewrite this expression as: x^{2} +3x -238

The middle term needs to be split into two terms whose product is -238x^{2} while the sum remains +3x

x^{2 }+ 17x - 14x -238

= x(x + 17) - 14 (x + 17)

= (x + 17) (x - 14)

### Example 70: Factorize the quadratic expression: x^{2} +6x -315

Let's rewrite this expression as: x^{2} +6x -315

The middle term needs to be split into two terms whose product is -315x^{2} while the sum remains +6x

x^{2 }- 15x + 21x -315

= x(x - 15) + 21 (x - 15)

= (x - 15) (x + 21)

### Example 71: Factorize the quadratic expression: x^{2} -8x -308

Let's rewrite this expression as: x^{2} -8x -308

The middle term needs to be split into two terms whose product is -308x^{2} while the sum remains -8x

x^{2 }- 22x + 14x -308

= x(x - 22) + 14 (x - 22)

= (x - 22) (x + 14)

### Example 72: Factorize the quadratic expression: x^{2} +9x -190

Let's rewrite this expression as: x^{2} +9x -190

The middle term needs to be split into two terms whose product is -190x^{2} while the sum remains +9x

x^{2 }- 10x + 19x -190

= x(x - 10) + 19 (x - 10)

= (x - 10) (x + 19)

### Example 73: Factorize the quadratic expression: x^{2} -11x -60

Let's rewrite this expression as: x^{2} -11x -60

The middle term needs to be split into two terms whose product is -60x^{2} while the sum remains -11x

x^{2 }+ 4x - 15x -60

= x(x + 4) - 15 (x + 4)

= (x + 4) (x - 15)

### Example 74: Factorize the quadratic expression: x^{2} +0x -25

Let's rewrite this expression as: x^{2} +0x -25

The middle term needs to be split into two terms whose product is -25x^{2} while the sum remains +0x

x^{2 }+ 5x - 5x -25

= x(x + 5) - 5 (x + 5)

= (x + 5) (x - 5)

### Example 75: Factorize the quadratic expression: x^{2} +45x +504

Let's rewrite this expression as: x^{2} +45x +504

The middle term needs to be split into two terms whose product is +504x^{2} while the sum remains +45x

x^{2 }+ 24x + 21x +504

= x(x + 24) + 21 (x + 24)

= (x + 24) (x + 21)

### Example 76: Factorize the quadratic expression: x^{2} +0x -289

Let's rewrite this expression as: x^{2} +0x -289

The middle term needs to be split into two terms whose product is -289x^{2} while the sum remains +0x

x^{2 }- 17x + 17x -289

= x(x - 17) + 17 (x - 17)

= (x - 17) (x + 17)

### Example 77: Factorize the quadratic expression: x^{2} -28x +196

Let's rewrite this expression as: x^{2} -28x +196

The middle term needs to be split into two terms whose product is +196x^{2} while the sum remains -28x

x^{2 }- 14x - 14x +196

= x(x - 14) - 14 (x - 14)

= (x - 14) (x - 14)

### Example 78: Factorize the quadratic expression: x^{2} -17x -18

Let's rewrite this expression as: x^{2} -17x -18

The middle term needs to be split into two terms whose product is -18x^{2} while the sum remains -17x

x^{2 }- 18x + 1x -18

= x(x - 18) + 1 (x - 18)

= (x - 18) (x + 1)

### Example 79: Factorize the quadratic expression: x^{2} -20x -96

Let's rewrite this expression as: x^{2} -20x -96

The middle term needs to be split into two terms whose product is -96x^{2} while the sum remains -20x

x^{2 }- 24x + 4x -96

= x(x - 24) + 4 (x - 24)

= (x - 24) (x + 4)

### Example 80: Factorize the quadratic expression: x^{2} +22x +117

Let's rewrite this expression as: x^{2} +22x +117

The middle term needs to be split into two terms whose product is +117x^{2} while the sum remains +22x

x^{2 }+ 9x + 13x +117

= x(x + 9) + 13 (x + 9)

= (x + 9) (x + 13)

### Example 81: Factorize the quadratic expression: x^{2} -11x -42

Let's rewrite this expression as: x^{2} -11x -42

The middle term needs to be split into two terms whose product is -42x^{2} while the sum remains -11x

x^{2 }+ 3x - 14x -42

= x(x + 3) - 14 (x + 3)

= (x + 3) (x - 14)

### Example 82: Factorize the quadratic expression: x^{2} -19x +18

Let's rewrite this expression as: x^{2} -19x +18

The middle term needs to be split into two terms whose product is +18x^{2} while the sum remains -19x

x^{2 }- 18x - 1x +18

= x(x - 18) - 1 (x - 18)

= (x - 18) (x - 1)

### Example 83: Factorize the quadratic expression: x^{2} -8x -384

Let's rewrite this expression as: x^{2} -8x -384

The middle term needs to be split into two terms whose product is -384x^{2} while the sum remains -8x

x^{2 }- 24x + 16x -384

= x(x - 24) + 16 (x - 24)

= (x - 24) (x + 16)

### Example 84: Factorize the quadratic expression: x^{2} +18x -63

Let's rewrite this expression as: x^{2} +18x -63

The middle term needs to be split into two terms whose product is -63x^{2} while the sum remains +18x

x^{2 }- 3x + 21x -63

= x(x - 3) + 21 (x - 3)

= (x - 3) (x + 21)

### Example 85: Factorize the quadratic expression: x^{2} -30x +221

Let's rewrite this expression as: x^{2} -30x +221

The middle term needs to be split into two terms whose product is +221x^{2} while the sum remains -30x

x^{2 }- 13x - 17x +221

= x(x - 13) - 17 (x - 13)

= (x - 13) (x - 17)

### Example 86: Factorize the quadratic expression: x^{2} +5x -456

Let's rewrite this expression as: x^{2} +5x -456

The middle term needs to be split into two terms whose product is -456x^{2} while the sum remains +5x

x^{2 }- 19x + 24x -456

= x(x - 19) + 24 (x - 19)

= (x - 19) (x + 24)

### Example 87: Factorize the quadratic expression: x^{2} -21x +80

Let's rewrite this expression as: x^{2} -21x +80

The middle term needs to be split into two terms whose product is +80x^{2} while the sum remains -21x

x^{2 }- 16x - 5x +80

= x(x - 16) - 5 (x - 16)

= (x - 16) (x - 5)

### Example 88: Factorize the quadratic expression: x^{2} -32x +207

Let's rewrite this expression as: x^{2} -32x +207

The middle term needs to be split into two terms whose product is +207x^{2} while the sum remains -32x

x^{2 }- 9x - 23x +207

= x(x - 9) - 23 (x - 9)

= (x - 9) (x - 23)

### Example 89: Factorize the quadratic expression: x^{2} +32x +240

Let's rewrite this expression as: x^{2} +32x +240

The middle term needs to be split into two terms whose product is +240x^{2} while the sum remains +32x

x^{2 }+ 20x + 12x +240

= x(x + 20) + 12 (x + 20)

= (x + 20) (x + 12)

### Example 90: Factorize the quadratic expression: x^{2} -2x -15

Let's rewrite this expression as: x^{2} -2x -15

The middle term needs to be split into two terms whose product is -15x^{2} while the sum remains -2x

x^{2 }- 5x + 3x -15

= x(x - 5) + 3 (x - 5)

= (x - 5) (x + 3)

### Example 91: Factorize the quadratic expression: x^{2} -37x +300

Let's rewrite this expression as: x^{2} -37x +300

The middle term needs to be split into two terms whose product is +300x^{2} while the sum remains -37x

x^{2 }- 25x - 12x +300

= x(x - 25) - 12 (x - 25)

= (x - 25) (x - 12)

### Example 92: Factorize the quadratic expression: x^{2} -21x +54

Let's rewrite this expression as: x^{2} -21x +54

The middle term needs to be split into two terms whose product is +54x^{2} while the sum remains -21x

x^{2 }- 18x - 3x +54

= x(x - 18) - 3 (x - 18)

= (x - 18) (x - 3)

### Example 93: Factorize the quadratic expression: x^{2} +26x +88

Let's rewrite this expression as: x^{2} +26x +88

The middle term needs to be split into two terms whose product is +88x^{2} while the sum remains +26x

x^{2 }+ 4x + 22x +88

= x(x + 4) + 22 (x + 4)

= (x + 4) (x + 22)

### Example 94: Factorize the quadratic expression: x^{2} -27x +72

Let's rewrite this expression as: x^{2} -27x +72

The middle term needs to be split into two terms whose product is +72x^{2} while the sum remains -27x

x^{2 }- 3x - 24x +72

= x(x - 3) - 24 (x - 3)

= (x - 3) (x - 24)

### Example 95: Factorize the quadratic expression: x^{2} -5x -6

Let's rewrite this expression as: x^{2} -5x -6

The middle term needs to be split into two terms whose product is -6x^{2} while the sum remains -5x

x^{2 }+ 1x - 6x -6

= x(x + 1) - 6 (x + 1)

= (x + 1) (x - 6)

### Example 96: Factorize the quadratic expression: x^{2} +10x -56

Let's rewrite this expression as: x^{2} +10x -56

The middle term needs to be split into two terms whose product is -56x^{2} while the sum remains +10x

x^{2 }- 4x + 14x -56

= x(x - 4) + 14 (x - 4)

= (x - 4) (x + 14)

### Example 97: Factorize the quadratic expression: x^{2} +12x +20

Let's rewrite this expression as: x^{2} +12x +20

The middle term needs to be split into two terms whose product is +20x^{2} while the sum remains +12x

x^{2 }+ 10x + 2x +20

= x(x + 10) + 2 (x + 10)

= (x + 10) (x + 2)

### Example 98: Factorize the quadratic expression: x^{2} -36x +323

Let's rewrite this expression as: x^{2} -36x +323

The middle term needs to be split into two terms whose product is +323x^{2} while the sum remains -36x

x^{2 }- 17x - 19x +323

= x(x - 17) - 19 (x - 17)

= (x - 17) (x - 19)

### Example 99: Factorize the quadratic expression: x^{2} +3x +2

Let's rewrite this expression as: x^{2} +3x +2

The middle term needs to be split into two terms whose product is +2x^{2} while the sum remains +3x

x^{2 }+ 2x + 1x +2

= x(x + 2) + 1 (x + 2)

= (x + 2) (x + 1)

### Example 100: Factorize the quadratic expression: x^{2} +36x +288

Let's rewrite this expression as: x^{2} +36x +288

The middle term needs to be split into two terms whose product is +288x^{2} while the sum remains +36x

x^{2 }+ 24x + 12x +288

= x(x + 24) + 12 (x + 24)

= (x + 24) (x + 12)