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Factorizing Quadratic Expressions By Splitting the Middle Terms

When splitting the middle term, our objective is to write quadratic expressions as the product of two linear polynomials.
The method for factoring by splitting the middle term is shown in detail in the following tutorial, in which we factor various examples of quadratic expressions.
Suppose you have a polynomial that can be factored as:
(Ax+B)(Cx+D)

Let's multiply this out and simplify the expression.

So in terms of the form ax2+bx+c we have:
a=AC
c=BD

In these examples we will start from the quadratic expression:

And we will try to factor it back into the form:
(Ax+B)(Cx+D)

The goal is to find some combination of factors of ABCD that add up to b=AD+BC

Example 1: Factorize the quadratic expression: x2 -8x -9

Let's rewrite this expression as: x2 -8x -9
The middle term needs to be split into two terms whose product is -9x2 while the sum remains -8x
x2 - 9x  + 1x  -9
= x(x - 9) + 1 (x - 9)
= (x - 9) (x + 1)

Example 2: Factorize the quadratic expression: x2 +13x -168

Let's rewrite this expression as: x2 +13x -168
The middle term needs to be split into two terms whose product is -168x2 while the sum remains +13x
x2 + 21x  - 8x  -168
= x(x + 21) - 8 (x + 21)
= (x + 21) (x - 8)

Example 3: Factorize the quadratic expression: x2 +3x -40

Let's rewrite this expression as: x2 +3x -40
The middle term needs to be split into two terms whose product is -40x2 while the sum remains +3x
x2 + 8x  - 5x  -40
= x(x + 8) - 5 (x + 8)
= (x + 8) (x - 5)

Example 4: Factorize the quadratic expression: x2 +5x -300

Let's rewrite this expression as: x2 +5x -300
The middle term needs to be split into two terms whose product is -300x2 while the sum remains +5x
x2 - 15x  + 20x  -300
= x(x - 15) + 20 (x - 15)
= (x - 15) (x + 20)

Example 5: Factorize the quadratic expression: x2 +32x +240

Let's rewrite this expression as: x2 +32x +240
The middle term needs to be split into two terms whose product is +240x2 while the sum remains +32x
x2 + 20x  + 12x  +240
= x(x + 20) + 12 (x + 20)
= (x + 20) (x + 12)

Example 6: Factorize the quadratic expression: x2 -15x -216

Let's rewrite this expression as: x2 -15x -216
The middle term needs to be split into two terms whose product is -216x2 while the sum remains -15x
x2 - 24x  + 9x  -216
= x(x - 24) + 9 (x - 24)
= (x - 24) (x + 9)

Example 7: Factorize the quadratic expression: x2 -39x +380

Let's rewrite this expression as: x2 -39x +380
The middle term needs to be split into two terms whose product is +380x2 while the sum remains -39x
x2 - 20x  - 19x  +380
= x(x - 20) - 19 (x - 20)
= (x - 20) (x - 19)

Example 8: Factorize the quadratic expression: x2 +22x +85

Let's rewrite this expression as: x2 +22x +85
The middle term needs to be split into two terms whose product is +85x2 while the sum remains +22x
x2 + 5x  + 17x  +85
= x(x + 5) + 17 (x + 5)
= (x + 5) (x + 17)

Example 9: Factorize the quadratic expression: x2 -13x -230

Let's rewrite this expression as: x2 -13x -230
The middle term needs to be split into two terms whose product is -230x2 while the sum remains -13x
x2 - 23x  + 10x  -230
= x(x - 23) + 10 (x - 23)
= (x - 23) (x + 10)

Example 10: Factorize the quadratic expression: x2 -15x -76

Let's rewrite this expression as: x2 -15x -76
The middle term needs to be split into two terms whose product is -76x2 while the sum remains -15x
x2 - 19x  + 4x  -76
= x(x - 19) + 4 (x - 19)
= (x - 19) (x + 4)

Example 11: Factorize the quadratic expression: x2 -17x +16

Let's rewrite this expression as: x2 -17x +16
The middle term needs to be split into two terms whose product is +16x2 while the sum remains -17x
x2 - 16x  - 1x  +16
= x(x - 16) - 1 (x - 16)
= (x - 16) (x - 1)

Example 12: Factorize the quadratic expression: x2 -21x +90

Let's rewrite this expression as: x2 -21x +90
The middle term needs to be split into two terms whose product is +90x2 while the sum remains -21x
x2 - 15x  - 6x  +90
= x(x - 15) - 6 (x - 15)
= (x - 15) (x - 6)

Example 13: Factorize the quadratic expression: x2 -7x -170

Let's rewrite this expression as: x2 -7x -170
The middle term needs to be split into two terms whose product is -170x2 while the sum remains -7x
x2 + 10x  - 17x  -170
= x(x + 10) - 17 (x + 10)
= (x + 10) (x - 17)

Example 14: Factorize the quadratic expression: x2 +7x -78

Let's rewrite this expression as: x2 +7x -78
The middle term needs to be split into two terms whose product is -78x2 while the sum remains +7x
x2 + 13x  - 6x  -78
= x(x + 13) - 6 (x + 13)
= (x + 13) (x - 6)

Example 15: Factorize the quadratic expression: x2 -44x +483

Let's rewrite this expression as: x2 -44x +483
The middle term needs to be split into two terms whose product is +483x2 while the sum remains -44x
x2 - 21x  - 23x  +483
= x(x - 21) - 23 (x - 21)
= (x - 21) (x - 23)

Example 16: Factorize the quadratic expression: x2 -6x -247

Let's rewrite this expression as: x2 -6x -247
The middle term needs to be split into two terms whose product is -247x2 while the sum remains -6x
x2 - 19x  + 13x  -247
= x(x - 19) + 13 (x - 19)
= (x - 19) (x + 13)

Example 17: Factorize the quadratic expression: x2 -14x -32

Let's rewrite this expression as: x2 -14x -32
The middle term needs to be split into two terms whose product is -32x2 while the sum remains -14x
x2 + 2x  - 16x  -32
= x(x + 2) - 16 (x + 2)
= (x + 2) (x - 16)

Example 18: Factorize the quadratic expression: x2 -8x -384

Let's rewrite this expression as: x2 -8x -384
The middle term needs to be split into two terms whose product is -384x2 while the sum remains -8x
x2 + 16x  - 24x  -384
= x(x + 16) - 24 (x + 16)
= (x + 16) (x - 24)

Example 19: Factorize the quadratic expression: x2 -10x -119

Let's rewrite this expression as: x2 -10x -119
The middle term needs to be split into two terms whose product is -119x2 while the sum remains -10x
x2 + 7x  - 17x  -119
= x(x + 7) - 17 (x + 7)
= (x + 7) (x - 17)

Example 20: Factorize the quadratic expression: x2 -9x -10

Let's rewrite this expression as: x2 -9x -10
The middle term needs to be split into two terms whose product is -10x2 while the sum remains -9x
x2 + 1x  - 10x  -10
= x(x + 1) - 10 (x + 1)
= (x + 1) (x - 10)

Example 21: Factorize the quadratic expression: x2 -25x +66

Let's rewrite this expression as: x2 -25x +66
The middle term needs to be split into two terms whose product is +66x2 while the sum remains -25x
x2 - 22x  - 3x  +66
= x(x - 22) - 3 (x - 22)
= (x - 22) (x - 3)

Example 22: Factorize the quadratic expression: x2 +27x +140

Let's rewrite this expression as: x2 +27x +140
The middle term needs to be split into two terms whose product is +140x2 while the sum remains +27x
x2 + 7x  + 20x  +140
= x(x + 7) + 20 (x + 7)
= (x + 7) (x + 20)

Example 23: Factorize the quadratic expression: x2 -6x -72

Let's rewrite this expression as: x2 -6x -72
The middle term needs to be split into two terms whose product is -72x2 while the sum remains -6x
x2 + 6x  - 12x  -72
= x(x + 6) - 12 (x + 6)
= (x + 6) (x - 12)

Example 24: Factorize the quadratic expression: x2 -7x -30

Let's rewrite this expression as: x2 -7x -30
The middle term needs to be split into two terms whose product is -30x2 while the sum remains -7x
x2 - 10x  + 3x  -30
= x(x - 10) + 3 (x - 10)
= (x - 10) (x + 3)

Example 25: Factorize the quadratic expression: x2 +13x -198

Let's rewrite this expression as: x2 +13x -198
The middle term needs to be split into two terms whose product is -198x2 while the sum remains +13x
x2 + 22x  - 9x  -198
= x(x + 22) - 9 (x + 22)
= (x + 22) (x - 9)

Example 26: Factorize the quadratic expression: x2 +32x +252

Let's rewrite this expression as: x2 +32x +252
The middle term needs to be split into two terms whose product is +252x2 while the sum remains +32x
x2 + 18x  + 14x  +252
= x(x + 18) + 14 (x + 18)
= (x + 18) (x + 14)

Example 27: Factorize the quadratic expression: x2 +17x -38

Let's rewrite this expression as: x2 +17x -38
The middle term needs to be split into two terms whose product is -38x2 while the sum remains +17x
x2 + 19x  - 2x  -38
= x(x + 19) - 2 (x + 19)
= (x + 19) (x - 2)

Example 28: Factorize the quadratic expression: x2 +2x -48

Let's rewrite this expression as: x2 +2x -48
The middle term needs to be split into two terms whose product is -48x2 while the sum remains +2x
x2 - 6x  + 8x  -48
= x(x - 6) + 8 (x - 6)
= (x - 6) (x + 8)

Example 29: Factorize the quadratic expression: x2 -20x -21

Let's rewrite this expression as: x2 -20x -21
The middle term needs to be split into two terms whose product is -21x2 while the sum remains -20x
x2 - 21x  + 1x  -21
= x(x - 21) + 1 (x - 21)
= (x - 21) (x + 1)

Example 30: Factorize the quadratic expression: x2 +28x +195

Let's rewrite this expression as: x2 +28x +195
The middle term needs to be split into two terms whose product is +195x2 while the sum remains +28x
x2 + 13x  + 15x  +195
= x(x + 13) + 15 (x + 13)
= (x + 13) (x + 15)

Example 31: Factorize the quadratic expression: x2 -21x -22

Let's rewrite this expression as: x2 -21x -22
The middle term needs to be split into two terms whose product is -22x2 while the sum remains -21x
x2 - 22x  + 1x  -22
= x(x - 22) + 1 (x - 22)
= (x - 22) (x + 1)

Example 32: Factorize the quadratic expression: x2 +24x +63

Let's rewrite this expression as: x2 +24x +63
The middle term needs to be split into two terms whose product is +63x2 while the sum remains +24x
x2 + 3x  + 21x  +63
= x(x + 3) + 21 (x + 3)
= (x + 3) (x + 21)

Example 33: Factorize the quadratic expression: x2 -10x -11

Let's rewrite this expression as: x2 -10x -11
The middle term needs to be split into two terms whose product is -11x2 while the sum remains -10x
x2 + 1x  - 11x  -11
= x(x + 1) - 11 (x + 1)
= (x + 1) (x - 11)

Example 34: Factorize the quadratic expression: x2 -29x +204

Let's rewrite this expression as: x2 -29x +204
The middle term needs to be split into two terms whose product is +204x2 while the sum remains -29x
x2 - 12x  - 17x  +204
= x(x - 12) - 17 (x - 12)
= (x - 12) (x - 17)

Example 35: Factorize the quadratic expression: x2 -6x -391

Let's rewrite this expression as: x2 -6x -391
The middle term needs to be split into two terms whose product is -391x2 while the sum remains -6x
x2 + 17x  - 23x  -391
= x(x + 17) - 23 (x + 17)
= (x + 17) (x - 23)

Example 36: Factorize the quadratic expression: x2 -28x +96

Let's rewrite this expression as: x2 -28x +96
The middle term needs to be split into two terms whose product is +96x2 while the sum remains -28x
x2 - 24x  - 4x  +96
= x(x - 24) - 4 (x - 24)
= (x - 24) (x - 4)

Example 37: Factorize the quadratic expression: x2 +20x +19

Let's rewrite this expression as: x2 +20x +19
The middle term needs to be split into two terms whose product is +19x2 while the sum remains +20x
x2 + 19x  + 1x  +19
= x(x + 19) + 1 (x + 19)
= (x + 19) (x + 1)

Example 38: Factorize the quadratic expression: x2 -32x +240

Let's rewrite this expression as: x2 -32x +240
The middle term needs to be split into two terms whose product is +240x2 while the sum remains -32x
x2 - 20x  - 12x  +240
= x(x - 20) - 12 (x - 20)
= (x - 20) (x - 12)

Example 39: Factorize the quadratic expression: x2 +13x -30

Let's rewrite this expression as: x2 +13x -30
The middle term needs to be split into two terms whose product is -30x2 while the sum remains +13x
x2 + 15x  - 2x  -30
= x(x + 15) - 2 (x + 15)
= (x + 15) (x - 2)

Example 40: Factorize the quadratic expression: x2 +3x -504

Let's rewrite this expression as: x2 +3x -504
The middle term needs to be split into two terms whose product is -504x2 while the sum remains +3x
x2 - 21x  + 24x  -504
= x(x - 21) + 24 (x - 21)
= (x - 21) (x + 24)

Example 41: Factorize the quadratic expression: x2 -11x -276

Let's rewrite this expression as: x2 -11x -276
The middle term needs to be split into two terms whose product is -276x2 while the sum remains -11x
x2 + 12x  - 23x  -276
= x(x + 12) - 23 (x + 12)
= (x + 12) (x - 23)

Example 42: Factorize the quadratic expression: x2 +7x -18

Let's rewrite this expression as: x2 +7x -18
The middle term needs to be split into two terms whose product is -18x2 while the sum remains +7x
x2 + 9x  - 2x  -18
= x(x + 9) - 2 (x + 9)
= (x + 9) (x - 2)

Example 43: Factorize the quadratic expression: x2 -29x +168

Let's rewrite this expression as: x2 -29x +168
The middle term needs to be split into two terms whose product is +168x2 while the sum remains -29x
x2 - 21x  - 8x  +168
= x(x - 21) - 8 (x - 21)
= (x - 21) (x - 8)

Example 44: Factorize the quadratic expression: x2 -22x +72

Let's rewrite this expression as: x2 -22x +72
The middle term needs to be split into two terms whose product is +72x2 while the sum remains -22x
x2 - 4x  - 18x  +72
= x(x - 4) - 18 (x - 4)
= (x - 4) (x - 18)

Example 45: Factorize the quadratic expression: x2 -9x +8

Let's rewrite this expression as: x2 -9x +8
The middle term needs to be split into two terms whose product is +8x2 while the sum remains -9x
x2 - 8x  - 1x  +8
= x(x - 8) - 1 (x - 8)
= (x - 8) (x - 1)

Example 46: Factorize the quadratic expression: x2 +4x +4

Let's rewrite this expression as: x2 +4x +4
The middle term needs to be split into two terms whose product is +4x2 while the sum remains +4x
x2 + 2x  + 2x  +4
= x(x + 2) + 2 (x + 2)
= (x + 2) (x + 2)

Example 47: Factorize the quadratic expression: x2 -15x -216

Let's rewrite this expression as: x2 -15x -216
The middle term needs to be split into two terms whose product is -216x2 while the sum remains -15x
x2 - 24x  + 9x  -216
= x(x - 24) + 9 (x - 24)
= (x - 24) (x + 9)

Example 48: Factorize the quadratic expression: x2 +32x +240

Let's rewrite this expression as: x2 +32x +240
The middle term needs to be split into two terms whose product is +240x2 while the sum remains +32x
x2 + 20x  + 12x  +240
= x(x + 20) + 12 (x + 20)
= (x + 20) (x + 12)

Example 49: Factorize the quadratic expression: x2 -20x +64

Let's rewrite this expression as: x2 -20x +64
The middle term needs to be split into two terms whose product is +64x2 while the sum remains -20x
x2 - 4x  - 16x  +64
= x(x - 4) - 16 (x - 4)
= (x - 4) (x - 16)

Example 50: Factorize the quadratic expression: x2 -49x +600

Let's rewrite this expression as: x2 -49x +600
The middle term needs to be split into two terms whose product is +600x2 while the sum remains -49x
x2 - 24x  - 25x  +600
= x(x - 24) - 25 (x - 24)
= (x - 24) (x - 25)

Example 51: Factorize the quadratic expression: x2 -12x -13

Let's rewrite this expression as: x2 -12x -13
The middle term needs to be split into two terms whose product is -13x2 while the sum remains -12x
x2 - 13x  + 1x  -13
= x(x - 13) + 1 (x - 13)
= (x - 13) (x + 1)

Example 52: Factorize the quadratic expression: x2 +23x +42

Let's rewrite this expression as: x2 +23x +42
The middle term needs to be split into two terms whose product is +42x2 while the sum remains +23x
x2 + 2x  + 21x  +42
= x(x + 2) + 21 (x + 2)
= (x + 2) (x + 21)

Example 53: Factorize the quadratic expression: x2 +11x -42

Let's rewrite this expression as: x2 +11x -42
The middle term needs to be split into two terms whose product is -42x2 while the sum remains +11x
x2 + 14x  - 3x  -42
= x(x + 14) - 3 (x + 14)
= (x + 14) (x - 3)

Example 54: Factorize the quadratic expression: x2 -23x +120

Let's rewrite this expression as: x2 -23x +120
The middle term needs to be split into two terms whose product is +120x2 while the sum remains -23x
x2 - 15x  - 8x  +120
= x(x - 15) - 8 (x - 15)
= (x - 15) (x - 8)

Example 55: Factorize the quadratic expression: x2 +16x +63

Let's rewrite this expression as: x2 +16x +63
The middle term needs to be split into two terms whose product is +63x2 while the sum remains +16x
x2 + 9x  + 7x  +63
= x(x + 9) + 7 (x + 9)
= (x + 9) (x + 7)

Example 56: Factorize the quadratic expression: x2 +17x +60

Let's rewrite this expression as: x2 +17x +60
The middle term needs to be split into two terms whose product is +60x2 while the sum remains +17x
x2 + 5x  + 12x  +60
= x(x + 5) + 12 (x + 5)
= (x + 5) (x + 12)

Example 57: Factorize the quadratic expression: x2 -27x +180

Let's rewrite this expression as: x2 -27x +180
The middle term needs to be split into two terms whose product is +180x2 while the sum remains -27x
x2 - 12x  - 15x  +180
= x(x - 12) - 15 (x - 12)
= (x - 12) (x - 15)

Example 58: Factorize the quadratic expression: x2 +17x +66

Let's rewrite this expression as: x2 +17x +66
The middle term needs to be split into two terms whose product is +66x2 while the sum remains +17x
x2 + 6x  + 11x  +66
= x(x + 6) + 11 (x + 6)
= (x + 6) (x + 11)

Example 59: Factorize the quadratic expression: x2 -2x -3

Let's rewrite this expression as: x2 -2x -3
The middle term needs to be split into two terms whose product is -3x2 while the sum remains -2x
x2 + 1x  - 3x  -3
= x(x + 1) - 3 (x + 1)
= (x + 1) (x - 3)

Example 60: Factorize the quadratic expression: x2 +10x -336

Let's rewrite this expression as: x2 +10x -336
The middle term needs to be split into two terms whose product is -336x2 while the sum remains +10x
x2 + 24x  - 14x  -336
= x(x + 24) - 14 (x + 24)
= (x + 24) (x - 14)

Example 61: Factorize the quadratic expression: x2 -25x +114

Let's rewrite this expression as: x2 -25x +114
The middle term needs to be split into two terms whose product is +114x2 while the sum remains -25x
x2 - 19x  - 6x  +114
= x(x - 19) - 6 (x - 19)
= (x - 19) (x - 6)

Example 62: Factorize the quadratic expression: x2 +12x -189

Let's rewrite this expression as: x2 +12x -189
The middle term needs to be split into two terms whose product is -189x2 while the sum remains +12x
x2 + 21x  - 9x  -189
= x(x + 21) - 9 (x + 21)
= (x + 21) (x - 9)

Example 63: Factorize the quadratic expression: x2 -8x -128

Let's rewrite this expression as: x2 -8x -128
The middle term needs to be split into two terms whose product is -128x2 while the sum remains -8x
x2 + 8x  - 16x  -128
= x(x + 8) - 16 (x + 8)
= (x + 8) (x - 16)

Example 64: Factorize the quadratic expression: x2 -12x -325

Let's rewrite this expression as: x2 -12x -325
The middle term needs to be split into two terms whose product is -325x2 while the sum remains -12x
x2 - 25x  + 13x  -325
= x(x - 25) + 13 (x - 25)
= (x - 25) (x + 13)

Example 65: Factorize the quadratic expression: x2 +10x +9

Let's rewrite this expression as: x2 +10x +9
The middle term needs to be split into two terms whose product is +9x2 while the sum remains +10x
x2 + 9x  + 1x  +9
= x(x + 9) + 1 (x + 9)
= (x + 9) (x + 1)

Example 66: Factorize the quadratic expression: x2 -3x -40

Let's rewrite this expression as: x2 -3x -40
The middle term needs to be split into two terms whose product is -40x2 while the sum remains -3x
x2 - 8x  + 5x  -40
= x(x - 8) + 5 (x - 8)
= (x - 8) (x + 5)

Example 67: Factorize the quadratic expression: x2 +40x +391

Let's rewrite this expression as: x2 +40x +391
The middle term needs to be split into two terms whose product is +391x2 while the sum remains +40x
x2 + 23x  + 17x  +391
= x(x + 23) + 17 (x + 23)
= (x + 23) (x + 17)

Example 68: Factorize the quadratic expression: x2 -18x +45

Let's rewrite this expression as: x2 -18x +45
The middle term needs to be split into two terms whose product is +45x2 while the sum remains -18x
x2 - 3x  - 15x  +45
= x(x - 3) - 15 (x - 3)
= (x - 3) (x - 15)

Example 69: Factorize the quadratic expression: x2 +3x -238

Let's rewrite this expression as: x2 +3x -238
The middle term needs to be split into two terms whose product is -238x2 while the sum remains +3x
x2 + 17x  - 14x  -238
= x(x + 17) - 14 (x + 17)
= (x + 17) (x - 14)

Example 70: Factorize the quadratic expression: x2 +6x -315

Let's rewrite this expression as: x2 +6x -315
The middle term needs to be split into two terms whose product is -315x2 while the sum remains +6x
x2 - 15x  + 21x  -315
= x(x - 15) + 21 (x - 15)
= (x - 15) (x + 21)

Example 71: Factorize the quadratic expression: x2 -8x -308

Let's rewrite this expression as: x2 -8x -308
The middle term needs to be split into two terms whose product is -308x2 while the sum remains -8x
x2 - 22x  + 14x  -308
= x(x - 22) + 14 (x - 22)
= (x - 22) (x + 14)

Example 72: Factorize the quadratic expression: x2 +9x -190

Let's rewrite this expression as: x2 +9x -190
The middle term needs to be split into two terms whose product is -190x2 while the sum remains +9x
x2 - 10x  + 19x  -190
= x(x - 10) + 19 (x - 10)
= (x - 10) (x + 19)

Example 73: Factorize the quadratic expression: x2 -11x -60

Let's rewrite this expression as: x2 -11x -60
The middle term needs to be split into two terms whose product is -60x2 while the sum remains -11x
x2 + 4x  - 15x  -60
= x(x + 4) - 15 (x + 4)
= (x + 4) (x - 15)

Example 74: Factorize the quadratic expression: x2 +0x -25

Let's rewrite this expression as: x2 +0x -25
The middle term needs to be split into two terms whose product is -25x2 while the sum remains +0x
x2 + 5x  - 5x  -25
= x(x + 5) - 5 (x + 5)
= (x + 5) (x - 5)

Example 75: Factorize the quadratic expression: x2 +45x +504

Let's rewrite this expression as: x2 +45x +504
The middle term needs to be split into two terms whose product is +504x2 while the sum remains +45x
x2 + 24x  + 21x  +504
= x(x + 24) + 21 (x + 24)
= (x + 24) (x + 21)

Example 76: Factorize the quadratic expression: x2 +0x -289

Let's rewrite this expression as: x2 +0x -289
The middle term needs to be split into two terms whose product is -289x2 while the sum remains +0x
x2 - 17x  + 17x  -289
= x(x - 17) + 17 (x - 17)
= (x - 17) (x + 17)

Example 77: Factorize the quadratic expression: x2 -28x +196

Let's rewrite this expression as: x2 -28x +196
The middle term needs to be split into two terms whose product is +196x2 while the sum remains -28x
x2 - 14x  - 14x  +196
= x(x - 14) - 14 (x - 14)
= (x - 14) (x - 14)

Example 78: Factorize the quadratic expression: x2 -17x -18

Let's rewrite this expression as: x2 -17x -18
The middle term needs to be split into two terms whose product is -18x2 while the sum remains -17x
x2 - 18x  + 1x  -18
= x(x - 18) + 1 (x - 18)
= (x - 18) (x + 1)

Example 79: Factorize the quadratic expression: x2 -20x -96

Let's rewrite this expression as: x2 -20x -96
The middle term needs to be split into two terms whose product is -96x2 while the sum remains -20x
x2 - 24x  + 4x  -96
= x(x - 24) + 4 (x - 24)
= (x - 24) (x + 4)

Example 80: Factorize the quadratic expression: x2 +22x +117

Let's rewrite this expression as: x2 +22x +117
The middle term needs to be split into two terms whose product is +117x2 while the sum remains +22x
x2 + 9x  + 13x  +117
= x(x + 9) + 13 (x + 9)
= (x + 9) (x + 13)

Example 81: Factorize the quadratic expression: x2 -11x -42

Let's rewrite this expression as: x2 -11x -42
The middle term needs to be split into two terms whose product is -42x2 while the sum remains -11x
x2 + 3x  - 14x  -42
= x(x + 3) - 14 (x + 3)
= (x + 3) (x - 14)

Example 82: Factorize the quadratic expression: x2 -19x +18

Let's rewrite this expression as: x2 -19x +18
The middle term needs to be split into two terms whose product is +18x2 while the sum remains -19x
x2 - 18x  - 1x  +18
= x(x - 18) - 1 (x - 18)
= (x - 18) (x - 1)

Example 83: Factorize the quadratic expression: x2 -8x -384

Let's rewrite this expression as: x2 -8x -384
The middle term needs to be split into two terms whose product is -384x2 while the sum remains -8x
x2 - 24x  + 16x  -384
= x(x - 24) + 16 (x - 24)
= (x - 24) (x + 16)

Example 84: Factorize the quadratic expression: x2 +18x -63

Let's rewrite this expression as: x2 +18x -63
The middle term needs to be split into two terms whose product is -63x2 while the sum remains +18x
x2 - 3x  + 21x  -63
= x(x - 3) + 21 (x - 3)
= (x - 3) (x + 21)

Example 85: Factorize the quadratic expression: x2 -30x +221

Let's rewrite this expression as: x2 -30x +221
The middle term needs to be split into two terms whose product is +221x2 while the sum remains -30x
x2 - 13x  - 17x  +221
= x(x - 13) - 17 (x - 13)
= (x - 13) (x - 17)

Example 86: Factorize the quadratic expression: x2 +5x -456

Let's rewrite this expression as: x2 +5x -456
The middle term needs to be split into two terms whose product is -456x2 while the sum remains +5x
x2 - 19x  + 24x  -456
= x(x - 19) + 24 (x - 19)
= (x - 19) (x + 24)

Example 87: Factorize the quadratic expression: x2 -21x +80

Let's rewrite this expression as: x2 -21x +80
The middle term needs to be split into two terms whose product is +80x2 while the sum remains -21x
x2 - 16x  - 5x  +80
= x(x - 16) - 5 (x - 16)
= (x - 16) (x - 5)

Example 88: Factorize the quadratic expression: x2 -32x +207

Let's rewrite this expression as: x2 -32x +207
The middle term needs to be split into two terms whose product is +207x2 while the sum remains -32x
x2 - 9x  - 23x  +207
= x(x - 9) - 23 (x - 9)
= (x - 9) (x - 23)

Example 89: Factorize the quadratic expression: x2 +32x +240

Let's rewrite this expression as: x2 +32x +240
The middle term needs to be split into two terms whose product is +240x2 while the sum remains +32x
x2 + 20x  + 12x  +240
= x(x + 20) + 12 (x + 20)
= (x + 20) (x + 12)

Example 90: Factorize the quadratic expression: x2 -2x -15

Let's rewrite this expression as: x2 -2x -15
The middle term needs to be split into two terms whose product is -15x2 while the sum remains -2x
x2 - 5x  + 3x  -15
= x(x - 5) + 3 (x - 5)
= (x - 5) (x + 3)

Example 91: Factorize the quadratic expression: x2 -37x +300

Let's rewrite this expression as: x2 -37x +300
The middle term needs to be split into two terms whose product is +300x2 while the sum remains -37x
x2 - 25x  - 12x  +300
= x(x - 25) - 12 (x - 25)
= (x - 25) (x - 12)

Example 92: Factorize the quadratic expression: x2 -21x +54

Let's rewrite this expression as: x2 -21x +54
The middle term needs to be split into two terms whose product is +54x2 while the sum remains -21x
x2 - 18x  - 3x  +54
= x(x - 18) - 3 (x - 18)
= (x - 18) (x - 3)

Example 93: Factorize the quadratic expression: x2 +26x +88

Let's rewrite this expression as: x2 +26x +88
The middle term needs to be split into two terms whose product is +88x2 while the sum remains +26x
x2 + 4x  + 22x  +88
= x(x + 4) + 22 (x + 4)
= (x + 4) (x + 22)

Example 94: Factorize the quadratic expression: x2 -27x +72

Let's rewrite this expression as: x2 -27x +72
The middle term needs to be split into two terms whose product is +72x2 while the sum remains -27x
x2 - 3x  - 24x  +72
= x(x - 3) - 24 (x - 3)
= (x - 3) (x - 24)

Example 95: Factorize the quadratic expression: x2 -5x -6

Let's rewrite this expression as: x2 -5x -6
The middle term needs to be split into two terms whose product is -6x2 while the sum remains -5x
x2 + 1x  - 6x  -6
= x(x + 1) - 6 (x + 1)
= (x + 1) (x - 6)

Example 96: Factorize the quadratic expression: x2 +10x -56

Let's rewrite this expression as: x2 +10x -56
The middle term needs to be split into two terms whose product is -56x2 while the sum remains +10x
x2 - 4x  + 14x  -56
= x(x - 4) + 14 (x - 4)
= (x - 4) (x + 14)

Example 97: Factorize the quadratic expression: x2 +12x +20

Let's rewrite this expression as: x2 +12x +20
The middle term needs to be split into two terms whose product is +20x2 while the sum remains +12x
x2 + 10x  + 2x  +20
= x(x + 10) + 2 (x + 10)
= (x + 10) (x + 2)

Example 98: Factorize the quadratic expression: x2 -36x +323

Let's rewrite this expression as: x2 -36x +323
The middle term needs to be split into two terms whose product is +323x2 while the sum remains -36x
x2 - 17x  - 19x  +323
= x(x - 17) - 19 (x - 17)
= (x - 17) (x - 19)

Example 99: Factorize the quadratic expression: x2 +3x +2

Let's rewrite this expression as: x2 +3x +2
The middle term needs to be split into two terms whose product is +2x2 while the sum remains +3x
x2 + 2x  + 1x  +2
= x(x + 2) + 1 (x + 2)
= (x + 2) (x + 1)

Example 100: Factorize the quadratic expression: x2 +36x +288

Let's rewrite this expression as: x2 +36x +288
The middle term needs to be split into two terms whose product is +288x2 while the sum remains +36x
x2 + 24x  + 12x  +288
= x(x + 24) + 12 (x + 24)
= (x + 24) (x + 12)