Question 1

Factor completely.
-$$x ^ { 2 } - x - 42$$

Accepted Answer

A)  $( x + 7 ) ( x - 6 )$ 
B)  $( x - 7 ) ( x + 7 )$ 
C)  $( x + 6 ) ( x - 7 )$ 
D)  $( x + 1 ) ( x - 13 )$ 
A)  $( x + 7 ) ( x - 6 )$ 
B)  $( x - 7 ) ( x + 7 )$ 
C)  $( x + 6 ) ( x - 7 )$ 
D)  $( x + 1 ) ( x - 13 )$

Question 2

Factor.
-$3 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }$

Accepted Answer

A)  $3 x ^ { 3 } ( x - 3 ) ( x + 4 )$ 
B)  $3 x ^ { 3 } ( x + 3 ) ( x - 4 )$ 
C)  $3 x ^ { 3 } ( x - 3 ) ( x - 4 )$ 
D)  $3 x ^ { 3 } ( x + 3 ) ( x + 4 )$ 
A)  $3 x ^ { 3 } ( x - 3 ) ( x + 4 )$ 
B)  $3 x ^ { 3 } ( x + 3 ) ( x - 4 )$ 
C)  $3 x ^ { 3 } ( x - 3 ) ( x - 4 )$ 
D)  $3 x ^ { 3 } ( x + 3 ) ( x + 4 )$

Question 3

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

Accepted Answer

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

Question 4

Factor.
-$$x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 25 }$$

Accepted Answer

A)  $\left( x + \frac { 4 } { 5 } \right) \left( x + \frac { 2 } { 5 } \right)$ 
B)  $\left( x + \frac { 2 } { 5 } \right) \left( x + \frac { 2 } { 5 } x \right)$ 
C)  $\left( x ^ { 2 } + \frac { 2 } { 5 } \right) ^ { 2 }$ 
D)  $\left( x + \frac { 2 } { 5 } \right) ^ { 2 }$ 
A)  $\left( x + \frac { 4 } { 5 } \right) \left( x + \frac { 2 } { 5 } \right)$ 
B)  $\left( x + \frac { 2 } { 5 } \right) \left( x + \frac { 2 } { 5 } x \right)$ 
C)  $\left( x ^ { 2 } + \frac { 2 } { 5 } \right) ^ { 2 }$ 
D)  $\left( x + \frac { 2 } { 5 } \right) ^ { 2 }$

Question 5

Determine whether the following is a difference of squares.
-$$x ^ { 2 } - 32$$

Accepted Answer

A) True 
 B)False

Question 6

Find the GCF.
-$$6 x ^ { 4 } , - 12 x$$

Accepted Answer

A)  $6 x ^ { 4 }$ 
B)  $- 12 x ^ { 4 }$ 
C)  $6 x$ 
D)  $4 \mathrm { x }$ 
A)  $6 x ^ { 4 }$ 
B)  $- 12 x ^ { 4 }$ 
C)  $6 x$ 
D)  $4 \mathrm { x }$

Question 7

Factor.
-$$t ^ { 2 } + 0.6 t + 0.09$$

Accepted Answer

A)  $t ( t + 0.6 )$ 
B)  $( t + 0.6 ) ^ { 2 }$ 
C)  $( t + 0.3 ) ^ { 2 }$ 
D)  $\left( t ^ { 2 } + 0.3 \right) ^ { 2 }$ 
A)  $t ( t + 0.6 )$ 
B)  $( t + 0.6 ) ^ { 2 }$ 
C)  $( t + 0.3 ) ^ { 2 }$ 
D)  $\left( t ^ { 2 } + 0.3 \right) ^ { 2 }$

Question 8

Factor completely.
-$50 x ^ { 2 } - 18 y ^ { 2 }$

Accepted Answer

A)  $( 5 x - 3 y ) ( 10 x + 6 y )$ 
B)  $( 10 x - 6 y ) ( 5 x + 3 y )$ 
C)  $2 ( 5 x - 3 y ) ( 5 x + 3 y )$ 
D)  $2 ( 5 x + 3 y ) ^ { 2 }$ 
A)  $( 5 x - 3 y ) ( 10 x + 6 y )$ 
B)  $( 10 x - 6 y ) ( 5 x + 3 y )$ 
C)  $2 ( 5 x - 3 y ) ( 5 x + 3 y )$ 
D)  $2 ( 5 x + 3 y ) ^ { 2 }$

Question 9

Factor completely.
-$$49 x ^ { 2 } + 70 x + 25$$

Accepted Answer

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

Question 10

Factor.
-$15 y ^ { 2 } + 16 y + 4$

Accepted Answer

A)  $( 3 y + 2 ) ( 5 y + 2 )$ 
B)  Prime 
C)  $( 15 y + 2 ) ( y + 2 )$ 
D)  $( 3 y - 2 ) ( 5 y - 2 )$ 
A)  $( 3 y + 2 ) ( 5 y + 2 )$ 
B)  Prime 
C)  $( 15 y + 2 ) ( y + 2 )$ 
D)  $( 3 y - 2 ) ( 5 y - 2 )$

Question 11

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

Accepted Answer

A)  $( 15 z + 2 ) ( z - 2 )$ 
B)  Prime 
C)  $( 3 z + 2 ) ( 5 z - 2 )$ 
D)  $( 3 z - 2 ) ( 5 z + 2 )$ 
A)  $( 15 z + 2 ) ( z - 2 )$ 
B)  Prime 
C)  $( 3 z + 2 ) ( 5 z - 2 )$ 
D)  $( 3 z - 2 ) ( 5 z + 2 )$

Question 12

Factor completely.
-$50 a ^ { 4 } - 8 b ^ { 2 }$

Accepted Answer

A)  $\left( 10 a ^ { 2 } + 4 b \right) \left( 5 a ^ { 2 } - 2 b \right)$ 
B)  $2 \left( 5 a ^ { 2 } + 2 b \right) ^ { 2 }$ 
C)  $2 \left( 5 a ^ { 2 } - 2 b \right) ^ { 2 }$ 
D)  $2 \left( 5 a ^ { 2 } + 2 b \right) \left( 5 a ^ { 2 } - 2 b \right)$ 
A)  $\left( 10 a ^ { 2 } + 4 b \right) \left( 5 a ^ { 2 } - 2 b \right)$ 
B)  $2 \left( 5 a ^ { 2 } + 2 b \right) ^ { 2 }$ 
C)  $2 \left( 5 a ^ { 2 } - 2 b \right) ^ { 2 }$ 
D)  $2 \left( 5 a ^ { 2 } + 2 b \right) \left( 5 a ^ { 2 } - 2 b \right)$

Question 13

Determine whether the following is a difference of squares.
-$$x ^ { 2 } - 100 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 14

Factor.
-$$84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$$

Accepted Answer

A)  $( 21 x + 7 y ) ( 4 x + y )$ 
B)  $7 ( 3 x + y ) ( 4 x + y )$ 
C)  $7 ( 3 x - y ) ( 4 x - y )$ 
D)  $( 3 x + y ) ( 7 x + 3 y )$ 
A)  $( 21 x + 7 y ) ( 4 x + y )$ 
B)  $7 ( 3 x + y ) ( 4 x + y )$ 
C)  $7 ( 3 x - y ) ( 4 x - y )$ 
D)  $( 3 x + y ) ( 7 x + 3 y )$

Question 15

Factor.
-$12 x ^ { 2 } - 52 x - 40$

Accepted Answer

A)  $4 ( 3 x + 2 ) ( x - 5 )$ 
B)  $( 12 x + 8 ) ( x - 5 )$ 
C)  $4 ( 3 x - 2 ) ( x + 5 )$ 
D)  $( 3 x + 2 ) ( 4 x - 20 )$ 
A)  $4 ( 3 x + 2 ) ( x - 5 )$ 
B)  $( 12 x + 8 ) ( x - 5 )$ 
C)  $4 ( 3 x - 2 ) ( x + 5 )$ 
D)  $( 3 x + 2 ) ( 4 x - 20 )$

Question 16

Find the GCF.
-$x ^ { 5 } y ^ { 5 } , x ^ { 4 } y ^ { 3 } , x ^ { 4 } y ^ { 4 } , - x y$

Accepted Answer

A)  $- x y$ 
B)  $x y$ 
C)  $x ^ { 3 } y ^ { 3 }$ 
D)  $x ^ { 4 } y ^ { 3 }$ 
A)  $- x y$ 
B)  $x y$ 
C)  $x ^ { 3 } y ^ { 3 }$ 
D)  $x ^ { 4 } y ^ { 3 }$

Question 17

Factor.
-$x ^ { 2 } + 5 x y - 14 y ^ { 2 }$

Accepted Answer

A)  $( x - y ) ( x + 2 y )$ 
B)  $( x + 7 y ) ( x - 2 y )$ 
C)  $( x - 7 y ) ( x + 2 y )$ 
D)  $( x - 7 y ) ( x + y )$ 
A)  $( x - y ) ( x + 2 y )$ 
B)  $( x + 7 y ) ( x - 2 y )$ 
C)  $( x - 7 y ) ( x + 2 y )$ 
D)  $( x - 7 y ) ( x + y )$

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

Factor.
-$$343 c ^ { 3 } + 216$$

Accepted Answer

A)  $( 7 c + 6 ) \left( 49 c ^ { 2 } + 36 \right)$ 
B)  $( 7 c - 6 ) \left( 49 c ^ { 2 } + 42 c + 36 \right)$ 
C)  $( 343 c + 6 ) \left( c ^ { 2 } - 42 c + 36 \right)$ 
D)  $( 7 c + 6 ) \left( 49 c ^ { 2 } - 42 c + 36 \right)$ 
A)  $( 7 c + 6 ) \left( 49 c ^ { 2 } + 36 \right)$ 
B)  $( 7 c - 6 ) \left( 49 c ^ { 2 } + 42 c + 36 \right)$ 
C)  $( 343 c + 6 ) \left( c ^ { 2 } - 42 c + 36 \right)$ 
D)  $( 7 c + 6 ) \left( 49 c ^ { 2 } - 42 c + 36 \right)$

Question 20

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

Accepted Answer

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

Factor completely. - $x ^ { 2 } - x - 42$

Factor. - $3 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }$

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

Factor. - $x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 25 }$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 32$

Find the GCF. - $6 x ^ { 4 } , - 12 x$

Factor. - $t ^ { 2 } + 0.6 t + 0.09$

Factor completely. - $50 x ^ { 2 } - 18 y ^ { 2 }$

Factor completely. - $49 x ^ { 2 } + 70 x + 25$

Factor. - $15 y ^ { 2 } + 16 y + 4$

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

Factor completely. - $50 a ^ { 4 } - 8 b ^ { 2 }$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 100 y ^ { 2 }$

Factor. - $84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$

Factor. - $12 x ^ { 2 } - 52 x - 40$

Find the GCF. - $x ^ { 5 } y ^ { 5 } , x ^ { 4 } y ^ { 3 } , x ^ { 4 } y ^ { 4 } , - x y$

Factor. - $x ^ { 2 } + 5 x y - 14 y ^ { 2 }$

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

Factor. - $343 c ^ { 3 } + 216$

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

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 completely. - x2−x−42x ^ { 2 } - x - 42x2−x−42

Factor. - 3x5−21x4+36x33 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }3x5−21x4+36x3

Factor. - x6−1x ^ { 6 } - 1x6−1

Factor. - x2+45x+425x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 25 }x2+54​x+254​

Determine whether the following is a difference of squares. - x2−32x ^ { 2 } - 32x2−32

Find the GCF. - 6x4,−12x6 x ^ { 4 } , - 12 x6x4,−12x

Factor. - t2+0.6t+0.09t ^ { 2 } + 0.6 t + 0.09t2+0.6t+0.09

Factor completely. - 50x2−18y250 x ^ { 2 } - 18 y ^ { 2 }50x2−18y2

Factor completely. - 49x2+70x+2549 x ^ { 2 } + 70 x + 2549x2+70x+25

Factor. - 15y2+16y+415 y ^ { 2 } + 16 y + 415y2+16y+4

Factor. - 15z2+4z−415 z ^ { 2 } + 4 z - 415z2+4z−4

Factor completely. - 50a4−8b250 a ^ { 4 } - 8 b ^ { 2 }50a4−8b2

Determine whether the following is a difference of squares. - x2−100y2x ^ { 2 } - 100 y ^ { 2 }x2−100y2

Factor. - 84x2+49xy+7y284 x ^ { 2 } + 49 x y + 7 y ^ { 2 }84x2+49xy+7y2

Factor. - 12x2−52x−4012 x ^ { 2 } - 52 x - 4012x2−52x−40

Find the GCF. - x5y5,x4y3,x4y4,−xyx ^ { 5 } y ^ { 5 } , x ^ { 4 } y ^ { 3 } , x ^ { 4 } y ^ { 4 } , - x yx5y5,x4y3,x4y4,−xy

Factor. - x2+5xy−14y2x ^ { 2 } + 5 x y - 14 y ^ { 2 }x2+5xy−14y2

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

Factor. - 343c3+216343 c ^ { 3 } + 216343c3+216

Factor. - x2+2xy−8y2x ^ { 2 } + 2 x y - 8 y ^ { 2 }x2+2xy−8y2

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 completely. - $x ^ { 2 } - x - 42$

Factor. - $3 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }$

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

Factor. - $x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 4 } { 25 }$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 32$

Find the GCF. - $6 x ^ { 4 } , - 12 x$

Factor. - $t ^ { 2 } + 0.6 t + 0.09$

Factor completely. - $50 x ^ { 2 } - 18 y ^ { 2 }$

Factor completely. - $49 x ^ { 2 } + 70 x + 25$

Factor. - $15 y ^ { 2 } + 16 y + 4$

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

Factor completely. - $50 a ^ { 4 } - 8 b ^ { 2 }$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 100 y ^ { 2 }$

Factor. - $84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$

Factor. - $12 x ^ { 2 } - 52 x - 40$

Find the GCF. - $x ^ { 5 } y ^ { 5 } , x ^ { 4 } y ^ { 3 } , x ^ { 4 } y ^ { 4 } , - x y$

Factor. - $x ^ { 2 } + 5 x y - 14 y ^ { 2 }$

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

Factor. - $343 c ^ { 3 } + 216$

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