Question 1

Factor.
-$$x ^ { 2 } + 4 x - 96$$

Accepted Answer

A)  $( x - 12 ) ( x + 1 )$ 
B)  $( x - 12 ) ( x + 8 )$ 
C)  Prime 
D)  $( x + 12 ) ( x - 8 )$ 
A)  $( x - 12 ) ( x + 1 )$ 
B)  $( x - 12 ) ( x + 8 )$ 
C)  Prime 
D)  $( x + 12 ) ( x - 8 )$

Question 2

Factor.
-$10 y - 30$

Accepted Answer

A)  No common factor 
B)  30 
C)  $10 y$ 
D)  $10 ( y - 3 )$ 
A)  No common factor 
B)  30 
C)  $10 y$ 
D)  $10 ( y - 3 )$

Question 3

Factor.
-$$x ^ { 2 } - 1.2 x + 0.35$$

Accepted Answer

A)  $( x - 0.7 ) ( x - 0.5 )$ 
B)  $( x - 0.7 ) ( x + 0.5 )$ 
C)  $( x - 0.6 ) ^ { 2 }$ 
D)  $( x + 0.7 ) ( x - 0.5 )$ 
A)  $( x - 0.7 ) ( x - 0.5 )$ 
B)  $( x - 0.7 ) ( x + 0.5 )$ 
C)  $( x - 0.6 ) ^ { 2 }$ 
D)  $( x + 0.7 ) ( x - 0.5 )$

Question 4

Factor completely.
-$$x ^ { 10 } + 12 x ^ { 5 } + 36$$

Accepted Answer

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

Question 5

Determine whether the following is a difference of squares.
-$$x ^ { 2 } - 36$$

Accepted Answer

A) True 
 B)False

Question 6

Factor.
-$$2 x ^ { 2 } - 14 x + 20$$

Accepted Answer

A)  $2 ( x - 10 ) ( x + 1 )$ 
B)  Prime 
C)  $2 ( x - 2 ) ( x - 5 )$ 
D)  $( 2 x - 4 ) ( x - 5 )$ 
A)  $2 ( x - 10 ) ( x + 1 )$ 
B)  Prime 
C)  $2 ( x - 2 ) ( x - 5 )$ 
D)  $( 2 x - 4 ) ( x - 5 )$

Question 7

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

Accepted Answer

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

Question 8

Factor.
-$49 - 126 x + 81 x ^ { 2 }$

Accepted Answer

A)  $( 81 x - 7 ) ( x - 7 )$ 
B)  $( 9 x + 7 ) ^ { 2 }$ 
C)  $( 9 x - 7 ) ^ { 2 }$ 
D)  Prime 
A)  $( 81 x - 7 ) ( x - 7 )$ 
B)  $( 9 x + 7 ) ^ { 2 }$ 
C)  $( 9 x - 7 ) ^ { 2 }$ 
D)  Prime

Question 9

Factor.
-$p ^ { 6 } - 64 y ^ { 6 }$

Accepted Answer

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

Question 10

Factor completely.
-$169 k ^ { 2 } - 36 m ^ { 2 }$

Accepted Answer

A)  $( 13 k - 6 m ) ^ { 2 }$ 
B)  $( 13 \mathrm { k } + 6 \mathrm {~m} ) ^ { 2 }$ 
C)  Prime 
D)  $( 13 k + 6 m ) ( 13 k - 6 m )$ 
A)  $( 13 k - 6 m ) ^ { 2 }$ 
B)  $( 13 \mathrm { k } + 6 \mathrm {~m} ) ^ { 2 }$ 
C)  Prime 
D)  $( 13 k + 6 m ) ( 13 k - 6 m )$

Question 11

Factor using the ac-method.
-$21 - 10 x + x ^ { 2 }$

Accepted Answer

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

Question 12

Factor.
-$$y ^ { 2 } - \frac { 2 } { 3 } y + \frac { 1 } { 9 }$$

Accepted Answer

A)  $\left( y + \frac { 1 } { 3 } \right) ^ { 2 }$ 
B)  Prime 
C)  $y \left( y - \frac { 2 } { 3 } \right)$ 
D)  $\left( y - \frac { 1 } { 3 } \right) ^ { 2 }$ 
A)  $\left( y + \frac { 1 } { 3 } \right) ^ { 2 }$ 
B)  Prime 
C)  $y \left( y - \frac { 2 } { 3 } \right)$ 
D)  $\left( y - \frac { 1 } { 3 } \right) ^ { 2 }$

Question 13

Factor.
-$125 y ^ { 9 } - z ^ { 9 }$

Accepted Answer

A)  $\left( 5 y ^ { 3 } - z ^ { 3 } \right) \left( 25 y + 5 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
B)  $\left( 25 y ^ { 3 } + z ^ { 3 } \right) \left( 5 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
C)  $\left( 25 y ^ { 3 } - z ^ { 3 } \right) \left( 5 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
D)  $\left( 5 y ^ { 3 } - z ^ { 3 } \right) \left( 25 y ^ { 6 } - 5 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
A)  $\left( 5 y ^ { 3 } - z ^ { 3 } \right) \left( 25 y + 5 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
B)  $\left( 25 y ^ { 3 } + z ^ { 3 } \right) \left( 5 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
C)  $\left( 25 y ^ { 3 } - z ^ { 3 } \right) \left( 5 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
D)  $\left( 5 y ^ { 3 } - z ^ { 3 } \right) \left( 25 y ^ { 6 } - 5 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$

Question 14

Factor using the ac-method.
-$$x ^ { 7 } - 5 x ^ { 6 } + 6 x ^ { 5 }$$

Accepted Answer

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

Question 15

Factor.
-$$12 z ^ { 6 } + 38 z ^ { 4 } + 20 z ^ { 2 }$$

Accepted Answer

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

Question 16

Factor.
-$$8 a ^ { 3 } - 27 b ^ { 3 }$$

Accepted Answer

A)  $\left( 2 a + 3 b ^ { 2 } \right) \left( 4 a ^ { 2 } - 6 a b + 9 b ^ { 2 } \right)$ 
B)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
C)  $( 8 a - 3 b ) \left( a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
D)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 9 b ^ { 2 } \right)$ 
A)  $\left( 2 a + 3 b ^ { 2 } \right) \left( 4 a ^ { 2 } - 6 a b + 9 b ^ { 2 } \right)$ 
B)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
C)  $( 8 a - 3 b ) \left( a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
D)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 9 b ^ { 2 } \right)$

Question 17

Factor completely.
-$$25 x ^ { 2 } - 20 x + 4 y ^ { 2 }$$

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Factor by grouping.
-$$x ^ { 3 } + 2 x ^ { 2 } - 10 x - 20$$

Accepted Answer

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

Question 20

Factor.
-$$u ^ { 2 } - 4 u v - 45 v ^ { 2 }$$

Accepted Answer

A)  $( u - 5 v ) ( u + v )$ 
B)  $( u - v ) ( u + 9 v )$ 
C)  $( u + 5 v ) ( u - 9 v )$ 
D)  $( u - 5 v ) ( u + 9 v )$ 
A)  $( u - 5 v ) ( u + v )$ 
B)  $( u - v ) ( u + 9 v )$ 
C)  $( u + 5 v ) ( u - 9 v )$ 
D)  $( u - 5 v ) ( u + 9 v )$

Factor. - $x ^ { 2 } + 4 x - 96$

Factor. - $10 y - 30$

Factor. - $x ^ { 2 } - 1.2 x + 0.35$

Factor completely. - $x ^ { 10 } + 12 x ^ { 5 } + 36$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 36$

Factor. - $2 x ^ { 2 } - 14 x + 20$

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

Factor. - $49 - 126 x + 81 x ^ { 2 }$

Factor. - $p ^ { 6 } - 64 y ^ { 6 }$

Factor completely. - $169 k ^ { 2 } - 36 m ^ { 2 }$

Factor using the ac-method. - $21 - 10 x + x ^ { 2 }$

Factor. - $y ^ { 2 } - \frac { 2 } { 3 } y + \frac { 1 } { 9 }$

Factor. - $125 y ^ { 9 } - z ^ { 9 }$

Factor using the ac-method. - $x ^ { 7 } - 5 x ^ { 6 } + 6 x ^ { 5 }$

Factor. - $12 z ^ { 6 } + 38 z ^ { 4 } + 20 z ^ { 2 }$

Factor. - $8 a ^ { 3 } - 27 b ^ { 3 }$

Factor completely. - $25 x ^ { 2 } - 20 x + 4 y ^ { 2 }$

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

Factor by grouping. - $x ^ { 3 } + 2 x ^ { 2 } - 10 x - 20$

Factor. - $u ^ { 2 } - 4 u v - 45 v ^ { 2 }$

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. - x2+4x−96x ^ { 2 } + 4 x - 96x2+4x−96

Factor. - 10y−3010 y - 3010y−30

Factor. - x2−1.2x+0.35x ^ { 2 } - 1.2 x + 0.35x2−1.2x+0.35

Factor completely. - x10+12x5+36x ^ { 10 } + 12 x ^ { 5 } + 36x10+12x5+36

Determine whether the following is a difference of squares. - x2−36x ^ { 2 } - 36x2−36

Factor. - 2x2−14x+202 x ^ { 2 } - 14 x + 202x2−14x+20

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

Factor. - 49−126x+81x249 - 126 x + 81 x ^ { 2 }49−126x+81x2

Factor. - p6−64y6p ^ { 6 } - 64 y ^ { 6 }p6−64y6

Factor completely. - 169k2−36m2169 k ^ { 2 } - 36 m ^ { 2 }169k2−36m2

Factor using the ac-method. - 21−10x+x221 - 10 x + x ^ { 2 }21−10x+x2

Factor. - y2−23y+19y ^ { 2 } - \frac { 2 } { 3 } y + \frac { 1 } { 9 }y2−32​y+91​

Factor. - 125y9−z9125 y ^ { 9 } - z ^ { 9 }125y9−z9

Factor using the ac-method. - x7−5x6+6x5x ^ { 7 } - 5 x ^ { 6 } + 6 x ^ { 5 }x7−5x6+6x5

Factor. - 12z6+38z4+20z212 z ^ { 6 } + 38 z ^ { 4 } + 20 z ^ { 2 }12z6+38z4+20z2

Factor. - 8a3−27b38 a ^ { 3 } - 27 b ^ { 3 }8a3−27b3

Factor completely. - 25x2−20x+4y225 x ^ { 2 } - 20 x + 4 y ^ { 2 }25x2−20x+4y2

Factor completely. - 9x2−42x+499 x ^ { 2 } - 42 x + 499x2−42x+49

Factor by grouping. - x3+2x2−10x−20x ^ { 3 } + 2 x ^ { 2 } - 10 x - 20x3+2x2−10x−20

Factor. - u2−4uv−45v2u ^ { 2 } - 4 u v - 45 v ^ { 2 }u2−4uv−45v2