Question 1

Factor using the ac-method.
-$10 z ^ { 2 } + 9 z - 9$

Accepted Answer

A)  $( 10 z + 3 ) ( z - 3 )$ 
B)  $( 2 z - 3 ) ( 5 z + 3 )$ 
C)  prime 
D)  $( 2 z + 3 ) ( 5 z - 3 )$ 
A)  $( 10 z + 3 ) ( z - 3 )$ 
B)  $( 2 z - 3 ) ( 5 z + 3 )$ 
C)  prime 
D)  $( 2 z + 3 ) ( 5 z - 3 )$

Question 2

Factor by grouping.
-$$x ^ { 3 } - 7 x ^ { 2 } - 8 x + 56$$

Accepted Answer

A)  $( x + 7 ) \left( x ^ { 2 } + 8 \right)$ 
B)  $( x - 7 ) \left( x ^ { 2 } - 8 \right)$ 
C)  $( x + 7 ) \left( x ^ { 3 } - 8 \right)$ 
D)  $( x - 7 ) \left( x ^ { 2 } + 8 x \right)$ 
A)  $( x + 7 ) \left( x ^ { 2 } + 8 \right)$ 
B)  $( x - 7 ) \left( x ^ { 2 } - 8 \right)$ 
C)  $( x + 7 ) \left( x ^ { 3 } - 8 \right)$ 
D)  $( x - 7 ) \left( x ^ { 2 } + 8 x \right)$

Question 3

Factor.
-$$9 x ^ { 2 } - 9 x - 54$$

Accepted Answer

A)  $( 9 x + 18 ) ( x - 3 )$ 
B)  $9 ( x - 2 ) ( x + 3 )$ 
C)  $9 ( x + 2 ) ( x - 3 )$ 
D)  Prime 
A)  $( 9 x + 18 ) ( x - 3 )$ 
B)  $9 ( x - 2 ) ( x + 3 )$ 
C)  $9 ( x + 2 ) ( x - 3 )$ 
D)  Prime

Question 4

Factor.
-$$\mathrm { x } ^ { 3 } - 27$$

Accepted Answer

A)  $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$ 
B)  $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$ 
C)  $( x + 27 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x - 3 ) \left( x ^ { 2 } + 9 \right)$ 
A)  $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$ 
B)  $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$ 
C)  $( x + 27 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x - 3 ) \left( x ^ { 2 } + 9 \right)$

Question 5

Factor.
-$20 z ^ { 2 } - 3 z - 9$

Accepted Answer

A)  $( 4 z + 3 ) ( 5 z - 3 )$ 
B)  Prime 
C)  $( 4 z - 3 ) ( 5 z + 3 )$ 
D)  $( 20 \mathrm { z } - 3 ) ( \mathrm { z } + 3 )$ 
A)  $( 4 z + 3 ) ( 5 z - 3 )$ 
B)  Prime 
C)  $( 4 z - 3 ) ( 5 z + 3 )$ 
D)  $( 20 \mathrm { z } - 3 ) ( \mathrm { z } + 3 )$

Question 6

Factor.
-$5 x ^ { 2 } - 5 x - 30$

Accepted Answer

A)  $5 ( x - 2 ) ( x + 3 )$ 
B)  $( x + 2 ) ( 5 x - 15 )$ 
C)  $( 5 x + 10 ) ( x - 3 )$ 
D)  $5 ( x + 2 ) ( x - 3 )$ 
A)  $5 ( x - 2 ) ( x + 3 )$ 
B)  $( x + 2 ) ( 5 x - 15 )$ 
C)  $( 5 x + 10 ) ( x - 3 )$ 
D)  $5 ( x + 2 ) ( x - 3 )$

Question 7

Factor.
-$$5 x ^ { 3 } + 5 x ^ { 2 } - 60 x$$

Accepted Answer

A)  Prime 
B)  $5 x ( x - 3 ) ( x + 4 )$ 
C)  $5 x ( x + 3 ) ( x - 4 )$ 
D)  $\left( 5 x ^ { 2 } + 15 x \right) ( x - 4 )$ 
A)  Prime 
B)  $5 x ( x - 3 ) ( x + 4 )$ 
C)  $5 x ( x + 3 ) ( x - 4 )$ 
D)  $\left( 5 x ^ { 2 } + 15 x \right) ( x - 4 )$

Question 8

Factor.
-$$6 x ^ { 3 } - 26 x ^ { 2 } - 20 x$$

Accepted Answer

A)  $2 x ( 3 x + 2 ) ( x - 5 )$ 
B)  $x ( 3 x + 2 ) ( 2 x - 10 )$ 
C)  $\left( x ^ { 2 } - 5 \right) ( 6 x + 4 )$ 
D)  $2 ( 3 x - 2 ) ( x + 5 )$ 
A)  $2 x ( 3 x + 2 ) ( x - 5 )$ 
B)  $x ( 3 x + 2 ) ( 2 x - 10 )$ 
C)  $\left( x ^ { 2 } - 5 \right) ( 6 x + 4 )$ 
D)  $2 ( 3 x - 2 ) ( x + 5 )$

Question 9

Factor.
-$$0.027 \mathrm { r } ^ { 3 } - 0.008 \mathrm {~s} ^ { 3 }$$

Accepted Answer

A)  $( 0.3 \mathrm { r } + 0.2 \mathrm {~s} ) \left( 0.09 \mathrm { r } ^ { 2 } - 0.06 \mathrm { rs } - 0.04 \mathrm {~s} ^ { 2 } \right)$ 
B)  $( 0.3 r + s ) \left( 0.018 r ^ { 2 } - 0.3 r s - 0.012 s ^ { 2 } \right)$ 
C)  $( 0.3 r - 0.2 \mathrm {~s} ) \left( 0.09 \mathrm { r } ^ { 2 } + 0.06 \mathrm { rs } + 0.04 \mathrm {~s} ^ { 2 } \right)$ 
D)  $( 0.3 r - s ) \left( 0.018 r ^ { 2 } + 0.3 r s + 0.012 s ^ { 2 } \right)$ 
A)  $( 0.3 \mathrm { r } + 0.2 \mathrm {~s} ) \left( 0.09 \mathrm { r } ^ { 2 } - 0.06 \mathrm { rs } - 0.04 \mathrm {~s} ^ { 2 } \right)$ 
B)  $( 0.3 r + s ) \left( 0.018 r ^ { 2 } - 0.3 r s - 0.012 s ^ { 2 } \right)$ 
C)  $( 0.3 r - 0.2 \mathrm {~s} ) \left( 0.09 \mathrm { r } ^ { 2 } + 0.06 \mathrm { rs } + 0.04 \mathrm {~s} ^ { 2 } \right)$ 
D)  $( 0.3 r - s ) \left( 0.018 r ^ { 2 } + 0.3 r s + 0.012 s ^ { 2 } \right)$

Question 10

Factor completely.
-$200 x ^ { 2 } + 160 x + 32$

Accepted Answer

A)  $( 40 x + 16 ) ( 5 x + 2 )$ 
B)  $8 \left( 25 x ^ { 2 } + 20 x + 4 \right)$ 
C)  $8 ( 5 x + 2 ) ^ { 2 }$ 
D)  $8 ( 5 x - 2 ) ( 5 x + 2 )$ 
A)  $( 40 x + 16 ) ( 5 x + 2 )$ 
B)  $8 \left( 25 x ^ { 2 } + 20 x + 4 \right)$ 
C)  $8 ( 5 x + 2 ) ^ { 2 }$ 
D)  $8 ( 5 x - 2 ) ( 5 x + 2 )$

Question 11

Determine whether the following is a trinomial square.
-$$x ^ { 2 } - 16 x + 256$$

Accepted Answer

A) True 
 B)False

Question 12

Factor using the ac-method.
-$$27 x ^ { 2 } - 117 x - 90$$

Accepted Answer

A)  prime 
B)  $9 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 27 x + 18 ) ( x - 5 )$ 
D)  $9 ( 3 x - 2 ) ( x + 5 )$ 
A)  prime 
B)  $9 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 27 x + 18 ) ( x - 5 )$ 
D)  $9 ( 3 x - 2 ) ( x + 5 )$

Question 13

Determine whether the following is a difference of squares.
-$$x ^ { 2 } + 1$$

Accepted Answer

A) True 
 B)False

Question 14

Determine whether the following is a difference of squares.
-$51 x ^ { 2 } - y ^ { 2 }$

Accepted Answer

A) True 
 B)False

Question 15

Factor.
-$25 m ^ { 2 } - 13 r ^ { 3 }$

Accepted Answer

A)  $3 \left( 8 m ^ { 2 } - 4 r ^ { 3 } \right)$ 
B)  $\mathrm { m } ^ { 2 } ( 25 - 13 \mathrm {~m} )$ 
C)  No common factor 
D)  $2 \left( 12 m ^ { 2 } + 6 r ^ { 3 } \right)$ 
A)  $3 \left( 8 m ^ { 2 } - 4 r ^ { 3 } \right)$ 
B)  $\mathrm { m } ^ { 2 } ( 25 - 13 \mathrm {~m} )$ 
C)  No common factor 
D)  $2 \left( 12 m ^ { 2 } + 6 r ^ { 3 } \right)$

Question 16

Factor by grouping.
-$$2 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 18$$

Accepted Answer

A)  Not possible 
B)  $( x - 3 ) \left( 2 x ^ { 2 } - 6 \right)$ 
C)  $( x + 18 ) \left( x ^ { 2 } - 6 x - 6 \right)$ 
D)  $( x + 3 ) \left( 2 x ^ { 2 } - 6 \right)$ 
A)  Not possible 
B)  $( x - 3 ) \left( 2 x ^ { 2 } - 6 \right)$ 
C)  $( x + 18 ) \left( x ^ { 2 } - 6 x - 6 \right)$ 
D)  $( x + 3 ) \left( 2 x ^ { 2 } - 6 \right)$

Question 17

Factor.
-$$10 x ^ { 3 } + 19 x ^ { 2 } + 6 x$$

Accepted Answer

A)  $x ( 10 x + 1 ) ( x + 6 )$ 
B)  $\left( 10 x ^ { 2 } + 3 \right) ( x + 2 )$ 
C)  $x ( 2 x + 3 ) ( 5 x + 2 )$ 
D)  $x ( 2 x - 3 ) ( 5 x - 2 )$ 
A)  $x ( 10 x + 1 ) ( x + 6 )$ 
B)  $\left( 10 x ^ { 2 } + 3 \right) ( x + 2 )$ 
C)  $x ( 2 x + 3 ) ( 5 x + 2 )$ 
D)  $x ( 2 x - 3 ) ( 5 x - 2 )$

Question 18

Determine whether the following is a trinomial square.
-$$x ^ { 2 } - 8 x + 64$$

Accepted Answer

A) True 
 B)False

Question 19

Factor.
-$12 x ^ { 2 } - 25 x y + 12 y ^ { 2 }$

Accepted Answer

A)  $( 12 x + 4 y ) ( x + 3 y )$ 
B)  $( 3 x - 4 y ) ( 4 x - 3 y )$ 
C)  $( 3 x + 4 y ) ( 4 x - 3 y )$ 
D)  $( 3 x + 4 y ) ( 4 x + 3 y )$ 
A)  $( 12 x + 4 y ) ( x + 3 y )$ 
B)  $( 3 x - 4 y ) ( 4 x - 3 y )$ 
C)  $( 3 x + 4 y ) ( 4 x - 3 y )$ 
D)  $( 3 x + 4 y ) ( 4 x + 3 y )$

Question 20

Factor.
-$7 x ^ { 2 } - 21 x y - 28 y ^ { 2 }$

Accepted Answer

A)  $( 7 x - 7 y ) ( x + 4 y )$ 
B)  $( x - y ) ( 7 x + 21 y )$ 
C)  $7 ( x - y ) ( x + 4 y )$ 
D)  $7 ( x + y ) ( x - 4 y )$ 
A)  $( 7 x - 7 y ) ( x + 4 y )$ 
B)  $( x - y ) ( 7 x + 21 y )$ 
C)  $7 ( x - y ) ( x + 4 y )$ 
D)  $7 ( x + y ) ( x - 4 y )$

Factor using the ac-method. - $10 z ^ { 2 } + 9 z - 9$

Factor by grouping. - $x ^ { 3 } - 7 x ^ { 2 } - 8 x + 56$

Factor. - $9 x ^ { 2 } - 9 x - 54$

Factor. - $\mathrm { x } ^ { 3 } - 27$

Factor. - $20 z ^ { 2 } - 3 z - 9$

Factor. - $5 x ^ { 2 } - 5 x - 30$

Factor. - $5 x ^ { 3 } + 5 x ^ { 2 } - 60 x$

Factor. - $6 x ^ { 3 } - 26 x ^ { 2 } - 20 x$

Factor. - $0.027 \mathrm { r } ^ { 3 } - 0.008 \mathrm {~s} ^ { 3 }$

Factor completely. - $200 x ^ { 2 } + 160 x + 32$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 16 x + 256$

Factor using the ac-method. - $27 x ^ { 2 } - 117 x - 90$

Determine whether the following is a difference of squares. - $x ^ { 2 } + 1$

Determine whether the following is a difference of squares. - $51 x ^ { 2 } - y ^ { 2 }$

Factor. - $25 m ^ { 2 } - 13 r ^ { 3 }$

Factor by grouping. - $2 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 18$

Factor. - $10 x ^ { 3 } + 19 x ^ { 2 } + 6 x$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 8 x + 64$

Factor. - $12 x ^ { 2 } - 25 x y + 12 y ^ { 2 }$

Factor. - $7 x ^ { 2 } - 21 x y - 28 y ^ { 2 }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 5: Polynomials: Factoring

Factor using the ac-method. - 10z2+9z−910 z ^ { 2 } + 9 z - 910z2+9z−9

Factor by grouping. - x3−7x2−8x+56x ^ { 3 } - 7 x ^ { 2 } - 8 x + 56x3−7x2−8x+56

Factor. - 9x2−9x−549 x ^ { 2 } - 9 x - 549x2−9x−54

Factor. - x3−27\mathrm { x } ^ { 3 } - 27x3−27

Factor. - 20z2−3z−920 z ^ { 2 } - 3 z - 920z2−3z−9

Factor. - 5x2−5x−305 x ^ { 2 } - 5 x - 305x2−5x−30

Factor. - 5x3+5x2−60x5 x ^ { 3 } + 5 x ^ { 2 } - 60 x5x3+5x2−60x

Factor. - 6x3−26x2−20x6 x ^ { 3 } - 26 x ^ { 2 } - 20 x6x3−26x2−20x

Factor. - 0.027r3−0.008 s30.027 \mathrm { r } ^ { 3 } - 0.008 \mathrm {~s} ^ { 3 }0.027r3−0.008 s3

Factor completely. - 200x2+160x+32200 x ^ { 2 } + 160 x + 32200x2+160x+32

Determine whether the following is a trinomial square. - x2−16x+256x ^ { 2 } - 16 x + 256x2−16x+256

Factor using the ac-method. - 27x2−117x−9027 x ^ { 2 } - 117 x - 9027x2−117x−90

Determine whether the following is a difference of squares. - x2+1x ^ { 2 } + 1x2+1

Determine whether the following is a difference of squares. - 51x2−y251 x ^ { 2 } - y ^ { 2 }51x2−y2

Factor. - 25m2−13r325 m ^ { 2 } - 13 r ^ { 3 }25m2−13r3

Factor by grouping. - 2x3−6x2−6x+182 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 182x3−6x2−6x+18

Factor. - 10x3+19x2+6x10 x ^ { 3 } + 19 x ^ { 2 } + 6 x10x3+19x2+6x

Determine whether the following is a trinomial square. - x2−8x+64x ^ { 2 } - 8 x + 64x2−8x+64

Factor. - 12x2−25xy+12y212 x ^ { 2 } - 25 x y + 12 y ^ { 2 }12x2−25xy+12y2

Factor. - 7x2−21xy−28y27 x ^ { 2 } - 21 x y - 28 y ^ { 2 }7x2−21xy−28y2

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Factor using the ac-method. - $10 z ^ { 2 } + 9 z - 9$

Factor by grouping. - $x ^ { 3 } - 7 x ^ { 2 } - 8 x + 56$

Factor. - $9 x ^ { 2 } - 9 x - 54$

Factor. - $\mathrm { x } ^ { 3 } - 27$

Factor. - $20 z ^ { 2 } - 3 z - 9$

Factor. - $5 x ^ { 2 } - 5 x - 30$

Factor. - $5 x ^ { 3 } + 5 x ^ { 2 } - 60 x$

Factor. - $6 x ^ { 3 } - 26 x ^ { 2 } - 20 x$

Factor. - $0.027 \mathrm { r } ^ { 3 } - 0.008 \mathrm {~s} ^ { 3 }$

Factor completely. - $200 x ^ { 2 } + 160 x + 32$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 16 x + 256$

Factor using the ac-method. - $27 x ^ { 2 } - 117 x - 90$

Determine whether the following is a difference of squares. - $x ^ { 2 } + 1$

Determine whether the following is a difference of squares. - $51 x ^ { 2 } - y ^ { 2 }$

Factor. - $25 m ^ { 2 } - 13 r ^ { 3 }$

Factor by grouping. - $2 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 18$

Factor. - $10 x ^ { 3 } + 19 x ^ { 2 } + 6 x$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 8 x + 64$

Factor. - $12 x ^ { 2 } - 25 x y + 12 y ^ { 2 }$

Factor. - $7 x ^ { 2 } - 21 x y - 28 y ^ { 2 }$