Question 1

Factor completely.
-$$81 m ^ { 2 } - \frac { 9 } { 16 }$$

Accepted Answer

A)  $\left( 9 m - \frac { 3 } { 4 } \right) ^ { 2 }$ 
B)  $\left( 9 m + \frac { 3 } { 4 } \right) \left( 9 m - \frac { 3 } { 4 } \right)$ 
C)  Prime 
D)  $\left( 9 m + \frac { 3 } { 4 } \right) ^ { 2 }$ 
A)  $\left( 9 m - \frac { 3 } { 4 } \right) ^ { 2 }$ 
B)  $\left( 9 m + \frac { 3 } { 4 } \right) \left( 9 m - \frac { 3 } { 4 } \right)$ 
C)  Prime 
D)  $\left( 9 m + \frac { 3 } { 4 } \right) ^ { 2 }$

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

Factor.
-$5 x ^ { 2 } - 15 x y - 20 y ^ { 2 }$

Accepted Answer

A)  $5 ( x - y ) ( x + 4 y )$ 
B)  $( 5 x - 5 y ) ( x + 4 y )$ 
C)  $( x - y ) ( 5 x + 15 y )$ 
D)  $5 ( x + y ) ( x - 4 y )$ 
A)  $5 ( x - y ) ( x + 4 y )$ 
B)  $( 5 x - 5 y ) ( x + 4 y )$ 
C)  $( x - y ) ( 5 x + 15 y )$ 
D)  $5 ( x + y ) ( x - 4 y )$

Question 4

Factor.
-$$y ^ { 2 } - \frac { 2 } { 5 } y + \frac { 1 } { 25 }$$

Accepted Answer

A)  $\left( y + \frac { 1 } { 5 } \right) ^ { 2 }$ 
B)  $\left( y - \frac { 1 } { 5 } \right) ^ { 2 }$ 
C)  Prime 
D)  $y \left( y - \frac { 2 } { 5 } \right)$ 
A)  $\left( y + \frac { 1 } { 5 } \right) ^ { 2 }$ 
B)  $\left( y - \frac { 1 } { 5 } \right) ^ { 2 }$ 
C)  Prime 
D)  $y \left( y - \frac { 2 } { 5 } \right)$

Question 5

Determine whether the following is a difference of squares.
-$$41 x ^ { 2 } - y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 6

Factor.
-$x ^ { 2 } - x - 72$

Accepted Answer

A)  $( x + 1 ) ( x - 72 )$ 
B)  $( x + 9 ) ( x - 8 )$ 
C)  Prime 
D)  $( x + 8 ) ( x - 9 )$ 
A)  $( x + 1 ) ( x - 72 )$ 
B)  $( x + 9 ) ( x - 8 )$ 
C)  Prime 
D)  $( x + 8 ) ( x - 9 )$

Question 7

Factor.
-$18 z ^ { 6 } - 15 z ^ { 4 } - 18 z ^ { 2 }$

Accepted Answer

A)  $\left( 6 z ^ { 3 } - 9 \right) \left( 3 z ^ { 3 } + 2 \right)$ 
B)  $3 z ^ { 2 } \left( 2 z ^ { 2 } - 3 \right) \left( 3 z ^ { 2 } + 2 \right)$ 
C)  $3 \left( 2 z ^ { 4 } - 3 \right) \left( 3 z ^ { 2 } + 2 \right)$ 
D)  $3 z ^ { 2 } \left( 3 z ^ { 2 } - 2 \right) \left( 2 z ^ { 2 } + 3 \right)$ 
A)  $\left( 6 z ^ { 3 } - 9 \right) \left( 3 z ^ { 3 } + 2 \right)$ 
B)  $3 z ^ { 2 } \left( 2 z ^ { 2 } - 3 \right) \left( 3 z ^ { 2 } + 2 \right)$ 
C)  $3 \left( 2 z ^ { 4 } - 3 \right) \left( 3 z ^ { 2 } + 2 \right)$ 
D)  $3 z ^ { 2 } \left( 3 z ^ { 2 } - 2 \right) \left( 2 z ^ { 2 } + 3 \right)$

Question 8

Factor completely.
-$$9 x ^ { 2 } - 42 x + 49 y ^ { 2 }$$

Accepted Answer

A)  $( 7 x - 3 y ) ^ { 2 }$ 
B)  $( 7 x + 3 y ) ^ { 2 }$ 
C)  $( 3 x - y ) ^ { 2 }$ 
D)  Prime 
A)  $( 7 x - 3 y ) ^ { 2 }$ 
B)  $( 7 x + 3 y ) ^ { 2 }$ 
C)  $( 3 x - y ) ^ { 2 }$ 
D)  Prime

Question 9

Factor completely.
-$$x ^ { 2 } - x - 20$$

Accepted Answer

A)  $( x - 5 ) ( x + 5 )$ 
B)  $( x + 5 ) ( x - 4 )$ 
C)  $( x + 4 ) ( x - 5 )$ 
D)  $( x + 1 ) ( x - 9 )$ 
A)  $( x - 5 ) ( x + 5 )$ 
B)  $( x + 5 ) ( x - 4 )$ 
C)  $( x + 4 ) ( x - 5 )$ 
D)  $( x + 1 ) ( x - 9 )$

Question 10

Factor.
-$20 x ^ { 2 } + 31 x y + 12 y ^ { 2 }$

Accepted Answer

A)  $( 20 x + 3 y ) ( x + 4 y )$ 
B)  $( 4 x + 3 y ) ( 5 x + 4 y )$ 
C)  $( 4 x - 3 y ) ( 5 x - 4 y )$ 
D)  $( 20 x + y ) ( x + 12 y )$ 
A)  $( 20 x + 3 y ) ( x + 4 y )$ 
B)  $( 4 x + 3 y ) ( 5 x + 4 y )$ 
C)  $( 4 x - 3 y ) ( 5 x - 4 y )$ 
D)  $( 20 x + y ) ( x + 12 y )$

Question 11

Factor.
-$27 a ^ { 3 } - 125 b ^ { 3 }$

Accepted Answer

A)  $( 3 a - 5 b ) \left( 9 a ^ { 2 } + 25 b ^ { 2 } \right)$ 
B)  $( 3 a - 5 b ) \left( 9 a ^ { 2 } + 15 a b + 25 b ^ { 2 } \right)$ 
C)  $( 27 a - 5 b ) \left( a ^ { 2 } + 15 a b + 25 b ^ { 2 } \right)$ 
D)  $\left( 3 a + 5 b ^ { 2 } \right) \left( 9 a ^ { 2 } - 15 a b + 25 b ^ { 2 } \right)$ 
A)  $( 3 a - 5 b ) \left( 9 a ^ { 2 } + 25 b ^ { 2 } \right)$ 
B)  $( 3 a - 5 b ) \left( 9 a ^ { 2 } + 15 a b + 25 b ^ { 2 } \right)$ 
C)  $( 27 a - 5 b ) \left( a ^ { 2 } + 15 a b + 25 b ^ { 2 } \right)$ 
D)  $\left( 3 a + 5 b ^ { 2 } \right) \left( 9 a ^ { 2 } - 15 a b + 25 b ^ { 2 } \right)$

Question 12

Factor using the ac-method.
-$6 x ^ { 2 } - 7 x t - 3 t ^ { 2 }$

Accepted Answer

A)  $( 3 x + t ) ( 2 x - 3 t )$ 
B)  prime 
C)  $( 3 x - t ) ( 2 x + 3 t )$ 
D)  $( 6 x + t ) ( x - 3 t )$ 
A)  $( 3 x + t ) ( 2 x - 3 t )$ 
B)  prime 
C)  $( 3 x - t ) ( 2 x + 3 t )$ 
D)  $( 6 x + t ) ( x - 3 t )$

Question 13

Factor.
-$\mathrm { t } ^ { 3 } + 8$

Accepted Answer

A)  $( t + 2 ) \left( t ^ { 2 } - 2 t + 4 \right)$ 
B)  $( \mathrm { t } - 2 ) \left( \mathrm { t } ^ { 2 } + 2 \mathrm { t } + 4 \right)$ 
C)  $( t - 8 ) \left( t ^ { 2 } - 1 \right)$ 
D)  $( t + 2 ) \left( t ^ { 2 } + 4 \right)$ 
A)  $( t + 2 ) \left( t ^ { 2 } - 2 t + 4 \right)$ 
B)  $( \mathrm { t } - 2 ) \left( \mathrm { t } ^ { 2 } + 2 \mathrm { t } + 4 \right)$ 
C)  $( t - 8 ) \left( t ^ { 2 } - 1 \right)$ 
D)  $( t + 2 ) \left( t ^ { 2 } + 4 \right)$

Question 14

Factor.
-$108 x ^ { 2 } + 63 x y + 9 y ^ { 2 }$

Accepted Answer

A)  $( 3 x + y ) ( 9 x + 3 y )$ 
B)  $( 27 x + 9 y ) ( 4 x + y )$ 
C)  $9 ( 3 x + y ) ( 4 x + y )$ 
D)  $9 ( 3 x - y ) ( 4 x - y )$ 
A)  $( 3 x + y ) ( 9 x + 3 y )$ 
B)  $( 27 x + 9 y ) ( 4 x + y )$ 
C)  $9 ( 3 x + y ) ( 4 x + y )$ 
D)  $9 ( 3 x - y ) ( 4 x - y )$

Question 15

Factor.
-$$31 - 72 x + 16 x ^ { 2 }$$

Accepted Answer

A)  $( 4 x - 9 ) ^ { 2 }$ 
B)  Prime 
C)  $( 4 x + 9 ) ^ { 2 }$ 
D)  $( 16 x - 9 ) ( x - 9 )$ 
A)  $( 4 x - 9 ) ^ { 2 }$ 
B)  Prime 
C)  $( 4 x + 9 ) ^ { 2 }$ 
D)  $( 16 x - 9 ) ( x - 9 )$

Question 16

Factor.
-$$15 z ^ { 4 } + 2 z ^ { 2 } - 8$$

Accepted Answer

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

Question 17

Factor.
-$$t ^ { 2 } + 0.1 t - 0.42$$

Accepted Answer

A)  $( t + 0.42 ) ( t - 1 )$ 
B)  $( t + 0.7 ) ( t - 0.6 )$ 
C)  $( t + 0.05 ) ^ { 2 }$ 
D)  $( t - 0.7 ) ( t + 0.6 )$ 
A)  $( t + 0.42 ) ( t - 1 )$ 
B)  $( t + 0.7 ) ( t - 0.6 )$ 
C)  $( t + 0.05 ) ^ { 2 }$ 
D)  $( t - 0.7 ) ( t + 0.6 )$

Question 18

Find the GCF.
-$$6 x ^ { 6 } , - 24 x ^ { 3 }$$

Accepted Answer

A)  $6 x ^ { 6 }$ 
B)  $2 x ^ { 3 }$ 
C)  $6 x ^ { 3 }$ 
D)  $- 24 x ^ { 6 }$ 
A)  $6 x ^ { 6 }$ 
B)  $2 x ^ { 3 }$ 
C)  $6 x ^ { 3 }$ 
D)  $- 24 x ^ { 6 }$

Question 19

Factor completely.
-$4 x ^ { 4 } - 4$

Accepted Answer

A)  $4 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ^ { 2 }$ 
B)  $4 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ( x - 1 )$ 
C)  $4 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 1 \right)$ 
D)  $4 \left( x ^ { 2 } + 1 \right) ( x - 1 ) ^ { 2 }$ 
A)  $4 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ^ { 2 }$ 
B)  $4 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ( x - 1 )$ 
C)  $4 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 1 \right)$ 
D)  $4 \left( x ^ { 2 } + 1 \right) ( x - 1 ) ^ { 2 }$

Question 20

Factor.
-$$x ^ { 6 } - 1$$

Accepted Answer

A)  $\left( x ^ { 3 } + 1 \right) \left( x ^ { 3 } - 1 \right)$ 
B)  $\left( x ^ { 2 } + 1 \right) \left( x ^ { 4 } - x ^ { 2 } + 1 \right)$ 
C)  $( x + 1 ) ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) \left( x ^ { 2 } - x + 1 \right)$ 
D)  $( x + 1 ) ( x - 1 ) \left( x ^ { 4 } + x ^ { 2 } + 1 \right)$ 
A)  $\left( x ^ { 3 } + 1 \right) \left( x ^ { 3 } - 1 \right)$ 
B)  $\left( x ^ { 2 } + 1 \right) \left( x ^ { 4 } - x ^ { 2 } + 1 \right)$ 
C)  $( x + 1 ) ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) \left( x ^ { 2 } - x + 1 \right)$ 
D)  $( x + 1 ) ( x - 1 ) \left( x ^ { 4 } + x ^ { 2 } + 1 \right)$

Factor completely. - $81 m ^ { 2 } - \frac { 9 } { 16 }$

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

Factor. - $5 x ^ { 2 } - 15 x y - 20 y ^ { 2 }$

Factor. - $y ^ { 2 } - \frac { 2 } { 5 } y + \frac { 1 } { 25 }$

Determine whether the following is a difference of squares. - $41 x ^ { 2 } - y ^ { 2 }$

Factor. - $x ^ { 2 } - x - 72$

Factor. - $18 z ^ { 6 } - 15 z ^ { 4 } - 18 z ^ { 2 }$

Factor completely. - $9 x ^ { 2 } - 42 x + 49 y ^ { 2 }$

Factor completely. - $x ^ { 2 } - x - 20$

Factor. - $20 x ^ { 2 } + 31 x y + 12 y ^ { 2 }$

Factor. - $27 a ^ { 3 } - 125 b ^ { 3 }$

Factor using the ac-method. - $6 x ^ { 2 } - 7 x t - 3 t ^ { 2 }$

Factor. - $\mathrm { t } ^ { 3 } + 8$

Factor. - $108 x ^ { 2 } + 63 x y + 9 y ^ { 2 }$

Factor. - $31 - 72 x + 16 x ^ { 2 }$

Factor. - $15 z ^ { 4 } + 2 z ^ { 2 } - 8$

Factor. - $t ^ { 2 } + 0.1 t - 0.42$

Find the GCF. - $6 x ^ { 6 } , - 24 x ^ { 3 }$

Factor completely. - $4 x ^ { 4 } - 4$

Factor. - $x ^ { 6 } - 1$

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

Filters

Exam 5: Polynomials: Factoring

Factor completely. - 81m2−91681 m ^ { 2 } - \frac { 9 } { 16 }81m2−169​

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

Factor. - 5x2−15xy−20y25 x ^ { 2 } - 15 x y - 20 y ^ { 2 }5x2−15xy−20y2

Factor. - y2−25y+125y ^ { 2 } - \frac { 2 } { 5 } y + \frac { 1 } { 25 }y2−52​y+251​

Determine whether the following is a difference of squares. - 41x2−y241 x ^ { 2 } - y ^ { 2 }41x2−y2

Factor. - x2−x−72x ^ { 2 } - x - 72x2−x−72

Factor. - 18z6−15z4−18z218 z ^ { 6 } - 15 z ^ { 4 } - 18 z ^ { 2 }18z6−15z4−18z2

Factor completely. - 9x2−42x+49y29 x ^ { 2 } - 42 x + 49 y ^ { 2 }9x2−42x+49y2

Factor completely. - x2−x−20x ^ { 2 } - x - 20x2−x−20

Factor. - 20x2+31xy+12y220 x ^ { 2 } + 31 x y + 12 y ^ { 2 }20x2+31xy+12y2

Factor. - 27a3−125b327 a ^ { 3 } - 125 b ^ { 3 }27a3−125b3

Factor using the ac-method. - 6x2−7xt−3t26 x ^ { 2 } - 7 x t - 3 t ^ { 2 }6x2−7xt−3t2

Factor. - t3+8\mathrm { t } ^ { 3 } + 8t3+8

Factor. - 108x2+63xy+9y2108 x ^ { 2 } + 63 x y + 9 y ^ { 2 }108x2+63xy+9y2

Factor. - 31−72x+16x231 - 72 x + 16 x ^ { 2 }31−72x+16x2

Factor. - 15z4+2z2−815 z ^ { 4 } + 2 z ^ { 2 } - 815z4+2z2−8

Factor. - t2+0.1t−0.42t ^ { 2 } + 0.1 t - 0.42t2+0.1t−0.42

Find the GCF. - 6x6,−24x36 x ^ { 6 } , - 24 x ^ { 3 }6x6,−24x3

Factor completely. - 4x4−44 x ^ { 4 } - 44x4−4

Factor. - x6−1x ^ { 6 } - 1x6−1