Question 1

Factor completely.
-$x ^ { 4 } - 1$

Accepted Answer

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

Question 2

Determine whether the following is a trinomial square.
-$$x ^ { 2 } + 12 x + 36$$

Accepted Answer

A) True 
 B)False

Question 3

Factor completely.
-$144 x ^ { 2 } + 48 x + 4$

Accepted Answer

A)  $( 24 x + 4 ) ( 6 x + 1 )$ 
B)  $4 ( 6 x - 1 ) ( 6 x + 1 )$ 
C)  $4 ( 6 x + 1 ) ^ { 2 }$ 
D)  $4 \left( 36 x ^ { 2 } + 12 x + 1 \right)$ 
A)  $( 24 x + 4 ) ( 6 x + 1 )$ 
B)  $4 ( 6 x - 1 ) ( 6 x + 1 )$ 
C)  $4 ( 6 x + 1 ) ^ { 2 }$ 
D)  $4 \left( 36 x ^ { 2 } + 12 x + 1 \right)$

Question 4

Factor.
-$24 m ^ { 9 } - 27 m ^ { 7 } - 24 m ^ { 5 }$

Accepted Answer

A)  No common factor 
B)  $m ^ { 5 } \left( 24 m ^ { 4 } - 27 m ^ { 2 } - 24 \right)$ 
C)  $3 \left( 8 m ^ { 9 } - 9 m ^ { 7 } - 8 m ^ { 5 } \right)$ 
D)  $3 m ^ { 5 } \left( 8 m ^ { 4 } - 9 m ^ { 2 } - 8 \right)$ 
A)  No common factor 
B)  $m ^ { 5 } \left( 24 m ^ { 4 } - 27 m ^ { 2 } - 24 \right)$ 
C)  $3 \left( 8 m ^ { 9 } - 9 m ^ { 7 } - 8 m ^ { 5 } \right)$ 
D)  $3 m ^ { 5 } \left( 8 m ^ { 4 } - 9 m ^ { 2 } - 8 \right)$

Question 5

Factor.
-$2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

Accepted Answer

A)  $2 ( x - y ) ( x + 4 y )$ 
B)  $( x - y ) ( 2 x + 6 y )$ 
C)  $( 2 x - 2 y ) ( x + 4 y )$ 
D)  $2 ( x + y ) ( x - 4 y )$ 
A)  $2 ( x - y ) ( x + 4 y )$ 
B)  $( x - y ) ( 2 x + 6 y )$ 
C)  $( 2 x - 2 y ) ( x + 4 y )$ 
D)  $2 ( x + y ) ( x - 4 y )$

Question 6

Factor completely.
-$49 y ^ { 4 } - 81$

Accepted Answer

A)  Prime 
B)  $\left( 7 y ^ { 2 } + 9 \right) \left( 7 y ^ { 2 } - 9 \right)$ 
C)  $\left( 7 y ^ { 2 } - 9 \right) ^ { 2 }$ 
D)  $\left( 7 y ^ { 2 } + 9 \right) ^ { 2 }$ 
A)  Prime 
B)  $\left( 7 y ^ { 2 } + 9 \right) \left( 7 y ^ { 2 } - 9 \right)$ 
C)  $\left( 7 y ^ { 2 } - 9 \right) ^ { 2 }$ 
D)  $\left( 7 y ^ { 2 } + 9 \right) ^ { 2 }$

Question 7

Factor.
-$80 z ^ { 8 } - 12 z ^ { 5 } - 36 z ^ { 2 }$

Accepted Answer

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

Question 8

Factor.
-$x ^ { 2 } - 7 x - 18$

Accepted Answer

A)  $( x - 2 ) ( x + 1 )$ 
B)  $( x + 2 ) ( x - 9 )$ 
C)  $( x - 2 ) ( x + 9 )$ 
D)  Prime 
A)  $( x - 2 ) ( x + 1 )$ 
B)  $( x + 2 ) ( x - 9 )$ 
C)  $( x - 2 ) ( x + 9 )$ 
D)  Prime

Question 9

Factor.
-$5 z ^ { 2 } - 5 z - 6$

Accepted Answer

A)  $( 3 z - 2 ) ( 2 z + 3 )$ 
B)  $( 3 z + 2 ) ( 2 z - 3 )$ 
C)  Prime 
D)  $( 6 z + 2 ) ( z - 3 )$ 
A)  $( 3 z - 2 ) ( 2 z + 3 )$ 
B)  $( 3 z + 2 ) ( 2 z - 3 )$ 
C)  Prime 
D)  $( 6 z + 2 ) ( z - 3 )$

Question 10

Factor.
-8y + 32

Accepted Answer

A) 32 
B) 8y 
C) No common factor 
D) 8(y + 4) 
A) 32 
B) 8y 
C) No common factor 
D) 8(y + 4)

Question 11

Factor completely.
-$175 x ^ { 2 } - 28$

Accepted Answer

A)  $( 35 x + 14 ) ( 5 x - 2 )$ 
B)  $7 ( 5 x + 2 ) ( 5 x - 2 )$ 
C)  $7 ( 5 x - 2 ) ^ { 2 }$ 
D)  $( 5 x + 2 ) ( 35 x - 14 )$ 
A)  $( 35 x + 14 ) ( 5 x - 2 )$ 
B)  $7 ( 5 x + 2 ) ( 5 x - 2 )$ 
C)  $7 ( 5 x - 2 ) ^ { 2 }$ 
D)  $( 5 x + 2 ) ( 35 x - 14 )$

Question 12

Factor completely.
-$$64 m ^ { 2 } - \frac { 4 } { 25 }$$

Accepted Answer

A)  $\left( 8 m - \frac { 2 } { 5 } \right) ^ { 2 }$ 
B)  prime 
C)  $\left( 8 m + \frac { 2 } { 5 } \right) ^ { 2 }$ 
D)  $\left( 8 m + \frac { 2 } { 5 } \right) \left( 8 m - \frac { 2 } { 5 } \right)$ 
A)  $\left( 8 m - \frac { 2 } { 5 } \right) ^ { 2 }$ 
B)  prime 
C)  $\left( 8 m + \frac { 2 } { 5 } \right) ^ { 2 }$ 
D)  $\left( 8 m + \frac { 2 } { 5 } \right) \left( 8 m - \frac { 2 } { 5 } \right)$

Question 13

Factor.
-$$4 x ^ { 2 } - 7 x + 8$$

Accepted Answer

A)  $( 2 x - 8 ) ( 2 x - 1 )$ 
B)  $( 4 x - 1 ) ( x - 8 )$ 
C)  $( 4 x - 8 ) ( x - 1 )$ 
D)  Prime 
A)  $( 2 x - 8 ) ( 2 x - 1 )$ 
B)  $( 4 x - 1 ) ( x - 8 )$ 
C)  $( 4 x - 8 ) ( x - 1 )$ 
D)  Prime

Question 14

Factor.
-$$x ^ { 2 } + \frac { 2 } { 7 } x + \frac { 1 } { 49 }$$

Accepted Answer

A)  Prime 
B)  $\left( x + \frac { 2 } { 7 } \right) ^ { 2 }$ 
C)  $x \left( x + \frac { 2 } { 7 } \right)$ 
D)  $\left( x + \frac { 1 } { 7 } \right) ^ { 2 }$ 
A)  Prime 
B)  $\left( x + \frac { 2 } { 7 } \right) ^ { 2 }$ 
C)  $x \left( x + \frac { 2 } { 7 } \right)$ 
D)  $\left( x + \frac { 1 } { 7 } \right) ^ { 2 }$

Question 15

Factor.
-$x ^ { 2 } + 3 x y - 28 y ^ { 2 }$

Accepted Answer

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

Question 16

Determine whether the following is a trinomial square.
-$$12 x ^ { 2 } - 52 x - 40$$

Accepted Answer

A) True 
 B)False

Question 17

Factor completely.
-$u ^ { 2 } - 3 u v - 54 v ^ { 2 }$

Accepted Answer

A)  $( u - 6 v ) ( u + v )$ 
B)  $( u - v ) ( u + 9 v )$ 
C)  $( u + 6 v ) ( u - 9 v )$ 
D)  $( u - 6 v ) ( u + 9 v )$ 
A)  $( u - 6 v ) ( u + v )$ 
B)  $( u - v ) ( u + 9 v )$ 
C)  $( u + 6 v ) ( u - 9 v )$ 
D)  $( u - 6 v ) ( u + 9 v )$

Question 18

Factor.
-$$a ^ { 6 } - 64 x ^ { 6 }$$

Accepted Answer

A)  $\left( a ^ { 3 } + 8 x ^ { 3 } \right) \left( a ^ { 3 } - 8 x ^ { 3 } \right)$ 
B)  $( a + 2 x ) ( a - 2 x ) \left( a ^ { 4 } + 4 a ^ { 2 } x ^ { 2 } + 16 x ^ { 4 } \right)$ 
C)  $\left( a ^ { 2 } - 4 x ^ { 2 } \right) \left( a ^ { 4 } + 4 a ^ { 2 } x ^ { 2 } + 16 x ^ { 4 } \right)$ 
D)  $( a + 2 x ) ( a - 2 x ) \left( a ^ { 2 } + 2 a x + 4 x ^ { 2 } \right) \left( a ^ { 2 } - 2 a x + 4 x ^ { 2 } \right)$ 
A)  $\left( a ^ { 3 } + 8 x ^ { 3 } \right) \left( a ^ { 3 } - 8 x ^ { 3 } \right)$ 
B)  $( a + 2 x ) ( a - 2 x ) \left( a ^ { 4 } + 4 a ^ { 2 } x ^ { 2 } + 16 x ^ { 4 } \right)$ 
C)  $\left( a ^ { 2 } - 4 x ^ { 2 } \right) \left( a ^ { 4 } + 4 a ^ { 2 } x ^ { 2 } + 16 x ^ { 4 } \right)$ 
D)  $( a + 2 x ) ( a - 2 x ) \left( a ^ { 2 } + 2 a x + 4 x ^ { 2 } \right) \left( a ^ { 2 } - 2 a x + 4 x ^ { 2 } \right)$

Question 19

Factor.
-$15 z ^ { 2 } - 14 z y - 8 y ^ { 2 }$

Accepted Answer

A)  $( 3 z - 4 y ) ( 5 z + 2 y )$ 
B)  $( 3 z + 4 y ) ( 5 z - 2 y )$ 
C)  $( 15 z + y ) ( z - 8 y )$ 
D)  $( 15 z - 4 y ) ( z + 2 y )$ 
A)  $( 3 z - 4 y ) ( 5 z + 2 y )$ 
B)  $( 3 z + 4 y ) ( 5 z - 2 y )$ 
C)  $( 15 z + y ) ( z - 8 y )$ 
D)  $( 15 z - 4 y ) ( z + 2 y )$

Question 20

Determine whether the following is a difference of squares.
-$$t ^ { 3 } - 36$$

Accepted Answer

A) True 
 B)False

Factor completely. - $x ^ { 4 } - 1$

Determine whether the following is a trinomial square. - $x ^ { 2 } + 12 x + 36$

Factor completely. - $144 x ^ { 2 } + 48 x + 4$

Factor. - $24 m ^ { 9 } - 27 m ^ { 7 } - 24 m ^ { 5 }$

Factor. - $2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

Factor completely. - $49 y ^ { 4 } - 81$

Factor. - $80 z ^ { 8 } - 12 z ^ { 5 } - 36 z ^ { 2 }$

Factor. - $x ^ { 2 } - 7 x - 18$

Factor. - $5 z ^ { 2 } - 5 z - 6$

Factor. -8y + 32

Factor completely. - $175 x ^ { 2 } - 28$

Factor completely. - $64 m ^ { 2 } - \frac { 4 } { 25 }$

Factor. - $4 x ^ { 2 } - 7 x + 8$

Factor. - $x ^ { 2 } + \frac { 2 } { 7 } x + \frac { 1 } { 49 }$

Factor. - $x ^ { 2 } + 3 x y - 28 y ^ { 2 }$

Determine whether the following is a trinomial square. - $12 x ^ { 2 } - 52 x - 40$

Factor completely. - $u ^ { 2 } - 3 u v - 54 v ^ { 2 }$

Factor. - $a ^ { 6 } - 64 x ^ { 6 }$

Factor. - $15 z ^ { 2 } - 14 z y - 8 y ^ { 2 }$

Determine whether the following is a difference of squares. - $t ^ { 3 } - 36$

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. - x4−1x ^ { 4 } - 1x4−1

Determine whether the following is a trinomial square. - x2+12x+36x ^ { 2 } + 12 x + 36x2+12x+36

Factor completely. - 144x2+48x+4144 x ^ { 2 } + 48 x + 4144x2+48x+4

Factor. - 24m9−27m7−24m524 m ^ { 9 } - 27 m ^ { 7 } - 24 m ^ { 5 }24m9−27m7−24m5

Factor. - 2x2−6xy−8y22 x ^ { 2 } - 6 x y - 8 y ^ { 2 }2x2−6xy−8y2

Factor completely. - 49y4−8149 y ^ { 4 } - 8149y4−81

Factor. - 80z8−12z5−36z280 z ^ { 8 } - 12 z ^ { 5 } - 36 z ^ { 2 }80z8−12z5−36z2

Factor. - x2−7x−18x ^ { 2 } - 7 x - 18x2−7x−18

Factor. - 5z2−5z−65 z ^ { 2 } - 5 z - 65z2−5z−6

Factor. -8y + 32

Factor completely. - 175x2−28175 x ^ { 2 } - 28175x2−28

Factor completely. - 64m2−42564 m ^ { 2 } - \frac { 4 } { 25 }64m2−254​

Factor. - 4x2−7x+84 x ^ { 2 } - 7 x + 84x2−7x+8

Factor. - x2+27x+149x ^ { 2 } + \frac { 2 } { 7 } x + \frac { 1 } { 49 }x2+72​x+491​

Factor. - x2+3xy−28y2x ^ { 2 } + 3 x y - 28 y ^ { 2 }x2+3xy−28y2

Determine whether the following is a trinomial square. - 12x2−52x−4012 x ^ { 2 } - 52 x - 4012x2−52x−40

Factor completely. - u2−3uv−54v2u ^ { 2 } - 3 u v - 54 v ^ { 2 }u2−3uv−54v2

Factor. - a6−64x6a ^ { 6 } - 64 x ^ { 6 }a6−64x6

Factor. - 15z2−14zy−8y215 z ^ { 2 } - 14 z y - 8 y ^ { 2 }15z2−14zy−8y2

Determine whether the following is a difference of squares. - t3−36t ^ { 3 } - 36t3−36

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

Factor completely. - $x ^ { 4 } - 1$

Determine whether the following is a trinomial square. - $x ^ { 2 } + 12 x + 36$

Factor completely. - $144 x ^ { 2 } + 48 x + 4$

Factor. - $24 m ^ { 9 } - 27 m ^ { 7 } - 24 m ^ { 5 }$

Factor. - $2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

Factor completely. - $49 y ^ { 4 } - 81$

Factor. - $80 z ^ { 8 } - 12 z ^ { 5 } - 36 z ^ { 2 }$

Factor. - $x ^ { 2 } - 7 x - 18$

Factor. - $5 z ^ { 2 } - 5 z - 6$

Factor completely. - $175 x ^ { 2 } - 28$

Factor completely. - $64 m ^ { 2 } - \frac { 4 } { 25 }$

Factor. - $4 x ^ { 2 } - 7 x + 8$

Factor. - $x ^ { 2 } + \frac { 2 } { 7 } x + \frac { 1 } { 49 }$

Factor. - $x ^ { 2 } + 3 x y - 28 y ^ { 2 }$

Determine whether the following is a trinomial square. - $12 x ^ { 2 } - 52 x - 40$

Factor completely. - $u ^ { 2 } - 3 u v - 54 v ^ { 2 }$

Factor. - $a ^ { 6 } - 64 x ^ { 6 }$

Factor. - $15 z ^ { 2 } - 14 z y - 8 y ^ { 2 }$

Determine whether the following is a difference of squares. - $t ^ { 3 } - 36$