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Evaluating Expressions Part 2

"Evaluation of an expression" generally means "simplifying an expression down to a final numerical value". In this lesson, we'll concentrate on the "plug" aspect of evaluation: plugging in values for variables, then computing the value of an expression for a given value of the variable.
These are examples of single variable functions below.
Usually the only difficult part in evaluation is in keeping track of the minus signs. It is strongly recommended to use parenthesis generously, for clarity and accuracy.
We will focus on polynomial functions in one variable, for now. These are higher order polynomials than those encountered in the first part.

Example 1: Consider the Polynomial: +13x4 -2x3 -11x2 +11x -15

Evaluate the expression for x=-4, x=-3, x=5, x=6, x=-12

Evaluating the given expression for x = -4
Let us compute. The required value = +13*(-4)4 -2*(-4)3 -11*(-4)2 +11*(-4) -15
=3221

Evaluating the given expression for x = -3
Let us compute. The required value = +13*(-3)4 -2*(-3)3 -11*(-3)2 +11*(-3) -15
=960

Evaluating the given expression for x = 5
Let us compute. The required value = +13*(5)4 -2*(5)3 -11*(5)2 +11*(5) -15
=7640

Evaluating the given expression for x = 6
Let us compute. The required value = +13*(6)4 -2*(6)3 -11*(6)2 +11*(6) -15
=16071

Evaluating the given expression for x = -12
Let us compute. The required value = +13*(-12)4 -2*(-12)3 -11*(-12)2 +11*(-12) -15
=271293

Example 2: Consider the Polynomial: -4x4 -3x3 -12x +6

Evaluate the expression for x=-20, x=12, x=-18, x=18, x=13

Evaluating the given expression for x = -20
Let us compute. The required value = -4*(-20)4 -3*(-20)3 -12*(-20) +6
=-615754

Evaluating the given expression for x = 12
Let us compute. The required value = -4*(12)4 -3*(12)3 -12*(12) +6
=-88266

Evaluating the given expression for x = -18
Let us compute. The required value = -4*(-18)4 -3*(-18)3 -12*(-18) +6
=-402186

Evaluating the given expression for x = 18
Let us compute. The required value = -4*(18)4 -3*(18)3 -12*(18) +6
=-437610

Evaluating the given expression for x = 13
Let us compute. The required value = -4*(13)4 -3*(13)3 -12*(13) +6
=-120985

Example 3: Consider the Polynomial: +11x4 -13x3 -14x2 +5x -5

Evaluate the expression for x=13, x=-12, x=-16, x=9, x=-14

Evaluating the given expression for x = 13
Let us compute. The required value = +11*(13)4 -13*(13)3 -14*(13)2 +5*(13) -5
=283304

Evaluating the given expression for x = -12
Let us compute. The required value = +11*(-12)4 -13*(-12)3 -14*(-12)2 +5*(-12) -5
=248479

Evaluating the given expression for x = -16
Let us compute. The required value = +11*(-16)4 -13*(-16)3 -14*(-16)2 +5*(-16) -5
=770475

Evaluating the given expression for x = 9
Let us compute. The required value = +11*(9)4 -13*(9)3 -14*(9)2 +5*(9) -5
=61600

Evaluating the given expression for x = -14
Let us compute. The required value = +11*(-14)4 -13*(-14)3 -14*(-14)2 +5*(-14) -5
=455429

Example 4: Consider the Polynomial: -7x4 +9x3 +4x2 -4x -15

Evaluate the expression for x=-16, x=-5, x=-3, x=-6

Evaluating the given expression for x = -16
Let us compute. The required value = -7*(-16)4 +9*(-16)3 +4*(-16)2 -4*(-16) -15
=-494543

Evaluating the given expression for x = -5
Let us compute. The required value = -7*(-5)4 +9*(-5)3 +4*(-5)2 -4*(-5) -15
=-5395

Evaluating the given expression for x = -3
Let us compute. The required value = -7*(-3)4 +9*(-3)3 +4*(-3)2 -4*(-3) -15
=-777

Evaluating the given expression for x = -6
Let us compute. The required value = -7*(-6)4 +9*(-6)3 +4*(-6)2 -4*(-6) -15
=-10863

Example 5: Consider the Polynomial: -5x4 +2x3 -9x2 +6x

Evaluate the expression for x=-19, x=1, x=11, x=-13, x=10

Evaluating the given expression for x = -19
Let us compute. The required value = -5*(-19)4 +2*(-19)3 -9*(-19)2 +6*(-19) (-19)0
=-668685

Evaluating the given expression for x = 1
Let us compute. The required value = -5*(1)4 +2*(1)3 -9*(1)2 +6*(1) (1)0
=-5

Evaluating the given expression for x = 11
Let us compute. The required value = -5*(11)4 +2*(11)3 -9*(11)2 +6*(11) (11)0
=-71565

Evaluating the given expression for x = -13
Let us compute. The required value = -5*(-13)4 +2*(-13)3 -9*(-13)2 +6*(-13) (-13)0
=-148797

Evaluating the given expression for x = 10
Let us compute. The required value = -5*(10)4 +2*(10)3 -9*(10)2 +6*(10) (10)0
=-48839

Example 6: Consider the Polynomial: +12x4 -12x3 +8x2 -2x

Evaluate the expression for x=15, x=-9, x=16, x=-4

Evaluating the given expression for x = 15
Let us compute. The required value = +12*(15)4 -12*(15)3 +8*(15)2 -2*(15) (15)0
=568771

Evaluating the given expression for x = -9
Let us compute. The required value = +12*(-9)4 -12*(-9)3 +8*(-9)2 -2*(-9) (-9)0
=88147

Evaluating the given expression for x = 16
Let us compute. The required value = +12*(16)4 -12*(16)3 +8*(16)2 -2*(16) (16)0
=739297

Evaluating the given expression for x = -4
Let us compute. The required value = +12*(-4)4 -12*(-4)3 +8*(-4)2 -2*(-4) (-4)0
=3977

Example 7: Consider the Polynomial: -8x4 -11x3 -12x2 +8x -11

Evaluate the expression for x=2, x=18, x=-19, x=-20, x=-1

Evaluating the given expression for x = 2
Let us compute. The required value = -8*(2)4 -11*(2)3 -12*(2)2 +8*(2) -11
=-259

Evaluating the given expression for x = 18
Let us compute. The required value = -8*(18)4 -11*(18)3 -12*(18)2 +8*(18) -11
=-907715

Evaluating the given expression for x = -19
Let us compute. The required value = -8*(-19)4 -11*(-19)3 -12*(-19)2 +8*(-19) -11
=-971614

Evaluating the given expression for x = -20
Let us compute. The required value = -8*(-20)4 -11*(-20)3 -12*(-20)2 +8*(-20) -11
=-1196971

Evaluating the given expression for x = -1
Let us compute. The required value = -8*(-1)4 -11*(-1)3 -12*(-1)2 +8*(-1) -11
=-28

Example 8: Consider the Polynomial: +12x4 +14x3 -8x2 +8x +12

Evaluate the expression for x=12, x=19, x=6, x=4

Evaluating the given expression for x = 12
Let us compute. The required value = +12*(12)4 +14*(12)3 -8*(12)2 +8*(12) +12
=271980

Evaluating the given expression for x = 19
Let us compute. The required value = +12*(19)4 +14*(19)3 -8*(19)2 +8*(19) +12
=1657154

Evaluating the given expression for x = 6
Let us compute. The required value = +12*(6)4 +14*(6)3 -8*(6)2 +8*(6) +12
=18348

Evaluating the given expression for x = 4
Let us compute. The required value = +12*(4)4 +14*(4)3 -8*(4)2 +8*(4) +12
=3884

Example 9: Consider the Polynomial: +12x4 -3x3 +14x2 -6x +3

Evaluate the expression for x=4, x=-9, x=7, x=1, x=8

Evaluating the given expression for x = 4
Let us compute. The required value = +12*(4)4 -3*(4)3 +14*(4)2 -6*(4) +3
=3083

Evaluating the given expression for x = -9
Let us compute. The required value = +12*(-9)4 -3*(-9)3 +14*(-9)2 -6*(-9) +3
=82110

Evaluating the given expression for x = 7
Let us compute. The required value = +12*(7)4 -3*(7)3 +14*(7)2 -6*(7) +3
=28430

Evaluating the given expression for x = 1
Let us compute. The required value = +12*(1)4 -3*(1)3 +14*(1)2 -6*(1) +3
=20

Evaluating the given expression for x = 8
Let us compute. The required value = +12*(8)4 -3*(8)3 +14*(8)2 -6*(8) +3
=48467

Example 10: Consider the Polynomial: -7x4 -5x3 +12x -15

Evaluate the expression for x=-16, x=-20, x=8, x=-6, x=-12

Evaluating the given expression for x = -16
Let us compute. The required value = -7*(-16)4 -5*(-16)3 +12*(-16) -15
=-438479

Evaluating the given expression for x = -20
Let us compute. The required value = -7*(-20)4 -5*(-20)3 +12*(-20) -15
=-1080255

Evaluating the given expression for x = 8
Let us compute. The required value = -7*(8)4 -5*(8)3 +12*(8) -15
=-31151

Evaluating the given expression for x = -6
Let us compute. The required value = -7*(-6)4 -5*(-6)3 +12*(-6) -15
=-8079

Evaluating the given expression for x = -12
Let us compute. The required value = -7*(-12)4 -5*(-12)3 +12*(-12) -15
=-136671

Example 11: Consider the Polynomial: -13x4 x3 +12x2 -4x +10

Evaluate the expression for x=-16, x=19, x=15, x=-19, x=9

Evaluating the given expression for x = -16
Let us compute. The required value = -13*(-16)4 (-16)3 +12*(-16)2 -4*(-16) +10
=-852918

Evaluating the given expression for x = 19
Let us compute. The required value = -13*(19)4 (19)3 +12*(19)2 -4*(19) +10
=-1683048

Evaluating the given expression for x = 15
Let us compute. The required value = -13*(15)4 (15)3 +12*(15)2 -4*(15) +10
=-652100

Evaluating the given expression for x = -19
Let us compute. The required value = -13*(-19)4 (-19)3 +12*(-19)2 -4*(-19) +10
=-1696614

Evaluating the given expression for x = 9
Let us compute. The required value = -13*(9)4 (9)3 +12*(9)2 -4*(9) +10
=-83618

Example 12: Consider the Polynomial: -4x4 +9x3 +5x2 +8x -3

Evaluate the expression for x=-11, x=8, x=-12, x=12

Evaluating the given expression for x = -11
Let us compute. The required value = -4*(-11)4 +9*(-11)3 +5*(-11)2 +8*(-11) -3
=-70029

Evaluating the given expression for x = 8
Let us compute. The required value = -4*(8)4 +9*(8)3 +5*(8)2 +8*(8) -3
=-11395

Evaluating the given expression for x = -12
Let us compute. The required value = -4*(-12)4 +9*(-12)3 +5*(-12)2 +8*(-12) -3
=-97875

Evaluating the given expression for x = 12
Let us compute. The required value = -4*(12)4 +9*(12)3 +5*(12)2 +8*(12) -3
=-66579

Example 13: Consider the Polynomial: -6x4 +7x3 +8x2 +5

Evaluate the expression for x=18, x=3, x=17, x=13, x=-18

Evaluating the given expression for x = 18
Let us compute. The required value = -6*(18)4 +7*(18)3 +8*(18)2 +5
=-586435

Evaluating the given expression for x = 3
Let us compute. The required value = -6*(3)4 +7*(3)3 +8*(3)2 +5
=-220

Evaluating the given expression for x = 17
Let us compute. The required value = -6*(17)4 +7*(17)3 +8*(17)2 +5
=-464418

Evaluating the given expression for x = 13
Let us compute. The required value = -6*(13)4 +7*(13)3 +8*(13)2 +5
=-154630

Evaluating the given expression for x = -18
Let us compute. The required value = -6*(-18)4 +7*(-18)3 +8*(-18)2 +5
=-668083

Example 14: Consider the Polynomial: +4x4 +13x3 -x2 -11x -10

Evaluate the expression for x=-3, x=6, x=-19, x=15, x=-4

Evaluating the given expression for x = -3
Let us compute. The required value = +4*(-3)4 +13*(-3)3 (-3)2 -11*(-3) -10
=-13

Evaluating the given expression for x = 6
Let us compute. The required value = +4*(6)4 +13*(6)3 (6)2 -11*(6) -10
=7880

Evaluating the given expression for x = -19
Let us compute. The required value = +4*(-19)4 +13*(-19)3 (-19)2 -11*(-19) -10
=431955

Evaluating the given expression for x = 15
Let us compute. The required value = +4*(15)4 +13*(15)3 (15)2 -11*(15) -10
=245975

Evaluating the given expression for x = -4
Let us compute. The required value = +4*(-4)4 +13*(-4)3 (-4)2 -11*(-4) -10
=210

Example 15: Consider the Polynomial: +14x4 -3x3 -5x2 -14x -3

Evaluate the expression for x=-13, x=-6, x=6, x=9, x=-2

Evaluating the given expression for x = -13
Let us compute. The required value = +14*(-13)4 -3*(-13)3 -5*(-13)2 -14*(-13) -3
=405779

Evaluating the given expression for x = -6
Let us compute. The required value = +14*(-6)4 -3*(-6)3 -5*(-6)2 -14*(-6) -3
=18693

Evaluating the given expression for x = 6
Let us compute. The required value = +14*(6)4 -3*(6)3 -5*(6)2 -14*(6) -3
=17229

Evaluating the given expression for x = 9
Let us compute. The required value = +14*(9)4 -3*(9)3 -5*(9)2 -14*(9) -3
=89133

Evaluating the given expression for x = -2
Let us compute. The required value = +14*(-2)4 -3*(-2)3 -5*(-2)2 -14*(-2) -3
=253

Example 16: Consider the Polynomial: x4 -7x3 -8x2 +5x +9

Evaluate the expression for x=6, x=11, x=16, x=-3, x=15

Evaluating the given expression for x = 6
Let us compute. The required value = (6)4 -7*(6)3 -8*(6)2 +5*(6) +9
=-465

Evaluating the given expression for x = 11
Let us compute. The required value = (11)4 -7*(11)3 -8*(11)2 +5*(11) +9
=4420

Evaluating the given expression for x = 16
Let us compute. The required value = (16)4 -7*(16)3 -8*(16)2 +5*(16) +9
=34905

Evaluating the given expression for x = -3
Let us compute. The required value = (-3)4 -7*(-3)3 -8*(-3)2 +5*(-3) +9
=192

Evaluating the given expression for x = 15
Let us compute. The required value = (15)4 -7*(15)3 -8*(15)2 +5*(15) +9
=25284

Example 17: Consider the Polynomial: +11x4 x3 -9x2 +6x -10

Evaluate the expression for x=4, x=14, x=-14, x=-16, x=1

Evaluating the given expression for x = 4
Let us compute. The required value = +11*(4)4 (4)3 -9*(4)2 +6*(4) -10
=2750

Evaluating the given expression for x = 14
Let us compute. The required value = +11*(14)4 (14)3 -9*(14)2 +6*(14) -10
=423630

Evaluating the given expression for x = -14
Let us compute. The required value = +11*(-14)4 (-14)3 -9*(-14)2 +6*(-14) -10
=417974

Evaluating the given expression for x = -16
Let us compute. The required value = +11*(-16)4 (-16)3 -9*(-16)2 +6*(-16) -10
=714390

Evaluating the given expression for x = 1
Let us compute. The required value = +11*(1)4 (1)3 -9*(1)2 +6*(1) -10
=-1

Example 18: Consider the Polynomial: +3x4 +2x3 -14x2 +6x +14

Evaluate the expression for x=2, x=19, x=-11, x=6

Evaluating the given expression for x = 2
Let us compute. The required value = +3*(2)4 +2*(2)3 -14*(2)2 +6*(2) +14
=34

Evaluating the given expression for x = 19
Let us compute. The required value = +3*(19)4 +2*(19)3 -14*(19)2 +6*(19) +14
=399755

Evaluating the given expression for x = -11
Let us compute. The required value = +3*(-11)4 +2*(-11)3 -14*(-11)2 +6*(-11) +14
=39515

Evaluating the given expression for x = 6
Let us compute. The required value = +3*(6)4 +2*(6)3 -14*(6)2 +6*(6) +14
=3866

Example 19: Consider the Polynomial: -10x3 -5x2 -12x +4

Evaluate the expression for x=-14, x=-8, x=7, x=-18, x=-3

Evaluating the given expression for x = -14
Let us compute. The required value = -10*(-14)3 -5*(-14)2 -12*(-14) +4
=26632

Evaluating the given expression for x = -8
Let us compute. The required value = -10*(-8)3 -5*(-8)2 -12*(-8) +4
=4900

Evaluating the given expression for x = 7
Let us compute. The required value = -10*(7)3 -5*(7)2 -12*(7) +4
=-3755

Evaluating the given expression for x = -18
Let us compute. The required value = -10*(-18)3 -5*(-18)2 -12*(-18) +4
=56920

Evaluating the given expression for x = -3
Let us compute. The required value = -10*(-3)3 -5*(-3)2 -12*(-3) +4
=265

Example 20: Consider the Polynomial: -12x4 -14x3 +7x2 +11x +8

Evaluate the expression for x=-7, x=17, x=11, x=12, x=9

Evaluating the given expression for x = -7
Let us compute. The required value = -12*(-7)4 -14*(-7)3 +7*(-7)2 +11*(-7) +8
=-23736

Evaluating the given expression for x = 17
Let us compute. The required value = -12*(17)4 -14*(17)3 +7*(17)2 +11*(17) +8
=-1068816

Evaluating the given expression for x = 11
Let us compute. The required value = -12*(11)4 -14*(11)3 +7*(11)2 +11*(11) +8
=-193350

Evaluating the given expression for x = 12
Let us compute. The required value = -12*(12)4 -14*(12)3 +7*(12)2 +11*(12) +8
=-271876

Evaluating the given expression for x = 9
Let us compute. The required value = -12*(9)4 -14*(9)3 +7*(9)2 +11*(9) +8
=-88264

Example 21: Consider the Polynomial: -12x4 -14x3 x2 -5x -12

Evaluate the expression for x=-10, x=-17, x=-1, x=-20, x=-5

Evaluating the given expression for x = -10
Let us compute. The required value = -12*(-10)4 -14*(-10)3 (-10)2 -5*(-10) -12
=-105862

Evaluating the given expression for x = -17
Let us compute. The required value = -12*(-17)4 -14*(-17)3 (-17)2 -5*(-17) -12
=-933108

Evaluating the given expression for x = -1
Let us compute. The required value = -12*(-1)4 -14*(-1)3 (-1)2 -5*(-1) -12
=-4

Evaluating the given expression for x = -20
Let us compute. The required value = -12*(-20)4 -14*(-20)3 (-20)2 -5*(-20) -12
=-1807512

Evaluating the given expression for x = -5
Let us compute. The required value = -12*(-5)4 -14*(-5)3 (-5)2 -5*(-5) -12
=-5712

Example 22: Consider the Polynomial: -12x4 +8x3 x2 +10x +7

Evaluate the expression for x=17, x=14, x=-9, x=8, x=-3

Evaluating the given expression for x = 17
Let us compute. The required value = -12*(17)4 +8*(17)3 (17)2 +10*(17) +7
=-962482

Evaluating the given expression for x = 14
Let us compute. The required value = -12*(14)4 +8*(14)3 (14)2 +10*(14) +7
=-438697

Evaluating the given expression for x = -9
Let us compute. The required value = -12*(-9)4 +8*(-9)3 (-9)2 +10*(-9) +7
=-84566

Evaluating the given expression for x = 8
Let us compute. The required value = -12*(8)4 +8*(8)3 (8)2 +10*(8) +7
=-44905

Evaluating the given expression for x = -3
Let us compute. The required value = -12*(-3)4 +8*(-3)3 (-3)2 +10*(-3) +7
=-1202

Example 23: Consider the Polynomial: -5x4 +3x3 -14x2 +8x +6

Evaluate the expression for x=4, x=-16, x=2, x=11, x=9

Evaluating the given expression for x = 4
Let us compute. The required value = -5*(4)4 +3*(4)3 -14*(4)2 +8*(4) +6
=-1274

Evaluating the given expression for x = -16
Let us compute. The required value = -5*(-16)4 +3*(-16)3 -14*(-16)2 +8*(-16) +6
=-343674

Evaluating the given expression for x = 2
Let us compute. The required value = -5*(2)4 +3*(2)3 -14*(2)2 +8*(2) +6
=-90

Evaluating the given expression for x = 11
Let us compute. The required value = -5*(11)4 +3*(11)3 -14*(11)2 +8*(11) +6
=-70812

Evaluating the given expression for x = 9
Let us compute. The required value = -5*(9)4 +3*(9)3 -14*(9)2 +8*(9) +6
=-31674

Example 24: Consider the Polynomial: -11x4 -2x3 -9x2 +7x +14

Evaluate the expression for x=-14, x=-5, x=6, x=-10, x=8

Evaluating the given expression for x = -14
Let us compute. The required value = -11*(-14)4 -2*(-14)3 -9*(-14)2 +7*(-14) +14
=-418936

Evaluating the given expression for x = -5
Let us compute. The required value = -11*(-5)4 -2*(-5)3 -9*(-5)2 +7*(-5) +14
=-6871

Evaluating the given expression for x = 6
Let us compute. The required value = -11*(6)4 -2*(6)3 -9*(6)2 +7*(6) +14
=-14956

Evaluating the given expression for x = -10
Let us compute. The required value = -11*(-10)4 -2*(-10)3 -9*(-10)2 +7*(-10) +14
=-108956

Evaluating the given expression for x = 8
Let us compute. The required value = -11*(8)4 -2*(8)3 -9*(8)2 +7*(8) +14
=-46586

Example 25: Consider the Polynomial: -6x4 -5x3 +11x2 +12x -10

Evaluate the expression for x=16, x=17, x=10, x=8

Evaluating the given expression for x = 16
Let us compute. The required value = -6*(16)4 -5*(16)3 +11*(16)2 +12*(16) -10
=-410698

Evaluating the given expression for x = 17
Let us compute. The required value = -6*(17)4 -5*(17)3 +11*(17)2 +12*(17) -10
=-522318

Evaluating the given expression for x = 10
Let us compute. The required value = -6*(10)4 -5*(10)3 +11*(10)2 +12*(10) -10
=-63790

Evaluating the given expression for x = 8
Let us compute. The required value = -6*(8)4 -5*(8)3 +11*(8)2 +12*(8) -10
=-26346