Question 1

Factor completely.
-$$36 x ^ { 2 } - 256$$

Accepted Answer

A)  $( 3 x - 8 ) ( 12 x + 32 )$ 
B)  $( 12 x - 32 ) ( 3 x + 8 )$ 
C)  $4 ( 3 x - 8 ) ( 3 x + 8 )$ 
D)  $4 ( 3 x + 8 ) ^ { 2 }$ 
A)  $( 3 x - 8 ) ( 12 x + 32 )$ 
B)  $( 12 x - 32 ) ( 3 x + 8 )$ 
C)  $4 ( 3 x - 8 ) ( 3 x + 8 )$ 
D)  $4 ( 3 x + 8 ) ^ { 2 }$

Question 2

Factor.
-$$x ^ { 2 } - 0.9 x + 0.14$$

Accepted Answer

A)  $( x + 0.7 ) ( x - 0.2 )$ 
B)  $( x - 0.7 ) ( x + 0.2 )$ 
C)  $( x - 0.7 ) ( x - 0.2 )$ 
D)  $( x - 0.45 ) ^ { 2 }$ 
A)  $( x + 0.7 ) ( x - 0.2 )$ 
B)  $( x - 0.7 ) ( x + 0.2 )$ 
C)  $( x - 0.7 ) ( x - 0.2 )$ 
D)  $( x - 0.45 ) ^ { 2 }$

Question 3

Factor completely.
-$$x ^ { 2 } - 32 x + 256$$

Accepted Answer

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

Question 4

Factor.
-$$u ^ { 2 } - 4 u v - 60 v ^ { 2 }$$

Accepted Answer

A)  $( u - 6 v ) ( u + 10 v )$ 
B)  $( u + 6 v ) ( u - 10 v )$ 
C)  $( u - 6 v ) ( u + v )$ 
D)  $( u - v ) ( u + 10 v )$ 
A)  $( u - 6 v ) ( u + 10 v )$ 
B)  $( u + 6 v ) ( u - 10 v )$ 
C)  $( u - 6 v ) ( u + v )$ 
D)  $( u - v ) ( u + 10 v )$

Question 5

Factor by grouping.
-$$x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24$$

Accepted Answer

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

Question 6

Factor.
-$15 z ^ { 2 } - 11 z - 12$

Accepted Answer

A)  $( 3 z + 4 ) ( 5 z - 3 )$ 
B)  $( 3 z - 4 ) ( 5 z + 3 )$ 
C)  $( 15 z - 4 ) ( z + 3 )$ 
D)  Prime 
A)  $( 3 z + 4 ) ( 5 z - 3 )$ 
B)  $( 3 z - 4 ) ( 5 z + 3 )$ 
C)  $( 15 z - 4 ) ( z + 3 )$ 
D)  Prime

Question 7

Factor.
-$12 m ^ { 2 } - 11 r ^ { 3 }$

Accepted Answer

A)  No common factor 
B)  $3 \left( 4 m ^ { 2 } - 3 r ^ { 3 } \right)$ 
C)  $m ^ { 2 } ( 12 - 11 \mathrm {~m} )$ 
D)  $2 \left( 6 m ^ { 2 } + 5 r ^ { 3 } \right)$ 
A)  No common factor 
B)  $3 \left( 4 m ^ { 2 } - 3 r ^ { 3 } \right)$ 
C)  $m ^ { 2 } ( 12 - 11 \mathrm {~m} )$ 
D)  $2 \left( 6 m ^ { 2 } + 5 r ^ { 3 } \right)$

Question 8

Factor.
-$175 \mathrm { x } ^ { 2 } + 560 \mathrm { xy } + 448 \mathrm { y } ^ { 2 }$

Accepted Answer

A)  $7 \left( 25 x ^ { 2 } + 80 x y + 64 y \right)$ 
B)  $7 ( 5 x + 8 y ) ^ { 2 }$ 
C)  $( 35 x + 56 y ) ( 5 x + 8 y )$ 
D)  $7 ( 5 x - 8 y ) ( 5 x + 8 y )$ 
A)  $7 \left( 25 x ^ { 2 } + 80 x y + 64 y \right)$ 
B)  $7 ( 5 x + 8 y ) ^ { 2 }$ 
C)  $( 35 x + 56 y ) ( 5 x + 8 y )$ 
D)  $7 ( 5 x - 8 y ) ( 5 x + 8 y )$

Question 9

Factor.
-$$5 x ^ { 2 } + 20 x$$

Accepted Answer

A)  $5 x ^ { 2 } ( x + 4 )$ 
B)  $x ( 5 x + 20 )$ 
C)  $5 x ( x + 4 )$ 
D)  $5 x ( x + 20 )$ 
A)  $5 x ^ { 2 } ( x + 4 )$ 
B)  $x ( 5 x + 20 )$ 
C)  $5 x ( x + 4 )$ 
D)  $5 x ( x + 20 )$

Question 10

Factor using the ac-method.
-$36 x ^ { 2 } + 21 x y + 3 y ^ { 2 }$

Accepted Answer

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

Question 11

Factor.
-$$u ^ { 2 } - 3 u v - 18 v ^ { 2 }$$

Accepted Answer

A)  $( u - 3 v ) ( u + v )$ 
B)  $( u + 3 v ) ( u - 6 v )$ 
C)  $( u - v ) ( u + 6 v )$ 
D)  $( u - 3 v ) ( u + 6 v )$ 
A)  $( u - 3 v ) ( u + v )$ 
B)  $( u + 3 v ) ( u - 6 v )$ 
C)  $( u - v ) ( u + 6 v )$ 
D)  $( u - 3 v ) ( u + 6 v )$

Question 12

Factor using the ac-method.
-$15 x ^ { 2 } + 22 x + 8$

Accepted Answer

A)  $( 15 x + 2 ) ( x + 4 )$ 
B)  $( 3 x - 2 ) ( 5 x - 4 )$ 
C)  prime 
D)  $( 3 x + 2 ) ( 5 x + 4 )$ 
A)  $( 15 x + 2 ) ( x + 4 )$ 
B)  $( 3 x - 2 ) ( 5 x - 4 )$ 
C)  prime 
D)  $( 3 x + 2 ) ( 5 x + 4 )$

Question 13

Factor using the ac-method.
-$x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 }$

Accepted Answer

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

Question 14

Factor using the ac-method.
-$21 x ^ { 2 } - 91 x - 70$

Accepted Answer

A)  $( 21 x + 14 ) ( x - 5 )$ 
B)  prime 
C)  $7 ( 3 x + 2 ) ( x - 5 )$ 
D)  $7 ( 3 x - 2 ) ( x + 5 )$ 
A)  $( 21 x + 14 ) ( x - 5 )$ 
B)  prime 
C)  $7 ( 3 x + 2 ) ( x - 5 )$ 
D)  $7 ( 3 x - 2 ) ( x + 5 )$

Question 15

Determine whether the following is a trinomial square.
-$$x ^ { 2 } - 12 x + 144$$

Accepted Answer

A) True 
 B)False

Question 16

Determine whether the following is a difference of squares.
-$$- 81 x ^ { 2 } + 81 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 17

Factor.
-$4 x ^ { 2 } - 32 x + 60$

Accepted Answer

A)  $4 ( x - 3 ) ( x - 5 )$ 
B)  $4 ( x - 15 ) ( x + 1 )$ 
C)  Prime 
D)  $( 4 x - 12 ) ( x - 5 )$ 
A)  $4 ( x - 3 ) ( x - 5 )$ 
B)  $4 ( x - 15 ) ( x + 1 )$ 
C)  Prime 
D)  $( 4 x - 12 ) ( x - 5 )$

Question 18

Factor by grouping.
-$$x ^ { 3 } - 8 x ^ { 2 } - 10 x + 80$$

Accepted Answer

A)  $( x - 8 ) \left( x ^ { 2 } - 10 \right)$ 
B)  $( x - 8 ) \left( x ^ { 2 } + 10 x \right)$ 
C)  $( x + 8 ) \left( x ^ { 2 } + 10 \right)$ 
D)  $( x + 8 ) \left( x ^ { 3 } - 10 \right)$ 
A)  $( x - 8 ) \left( x ^ { 2 } - 10 \right)$ 
B)  $( x - 8 ) \left( x ^ { 2 } + 10 x \right)$ 
C)  $( x + 8 ) \left( x ^ { 2 } + 10 \right)$ 
D)  $( x + 8 ) \left( x ^ { 3 } - 10 \right)$

Question 19

Factor completely.
-$50 a ^ { 4 } b - 72 b ^ { 3 }$

Accepted Answer

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

Question 20

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)  $\left( x + \frac { 2 } { 5 } \right) ^ { 2 }$

Factor completely. - $36 x ^ { 2 } - 256$

Factor. - $x ^ { 2 } - 0.9 x + 0.14$

Factor completely. - $x ^ { 2 } - 32 x + 256$

Factor. - $u ^ { 2 } - 4 u v - 60 v ^ { 2 }$

Factor by grouping. - $x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24$

Factor. - $15 z ^ { 2 } - 11 z - 12$

Factor. - $12 m ^ { 2 } - 11 r ^ { 3 }$

Factor. - $175 \mathrm { x } ^ { 2 } + 560 \mathrm { xy } + 448 \mathrm { y } ^ { 2 }$

Factor. - $5 x ^ { 2 } + 20 x$

Factor using the ac-method. - $36 x ^ { 2 } + 21 x y + 3 y ^ { 2 }$

Factor. - $u ^ { 2 } - 3 u v - 18 v ^ { 2 }$

Factor using the ac-method. - $15 x ^ { 2 } + 22 x + 8$

Factor using the ac-method. - $x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 }$

Factor using the ac-method. - $21 x ^ { 2 } - 91 x - 70$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 12 x + 144$

Determine whether the following is a difference of squares. - $- 81 x ^ { 2 } + 81 y ^ { 2 }$

Factor. - $4 x ^ { 2 } - 32 x + 60$

Factor by grouping. - $x ^ { 3 } - 8 x ^ { 2 } - 10 x + 80$

Factor completely. - $50 a ^ { 4 } b - 72 b ^ { 3 }$

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

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. - 36x2−25636 x ^ { 2 } - 25636x2−256

Factor. - x2−0.9x+0.14x ^ { 2 } - 0.9 x + 0.14x2−0.9x+0.14

Factor completely. - x2−32x+256x ^ { 2 } - 32 x + 256x2−32x+256

Factor. - u2−4uv−60v2u ^ { 2 } - 4 u v - 60 v ^ { 2 }u2−4uv−60v2

Factor by grouping. - x3−6x2+4x−24x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24x3−6x2+4x−24

Factor. - 15z2−11z−1215 z ^ { 2 } - 11 z - 1215z2−11z−12

Factor. - 12m2−11r312 m ^ { 2 } - 11 r ^ { 3 }12m2−11r3

Factor. - 175x2+560xy+448y2175 \mathrm { x } ^ { 2 } + 560 \mathrm { xy } + 448 \mathrm { y } ^ { 2 }175x2+560xy+448y2

Factor. - 5x2+20x5 x ^ { 2 } + 20 x5x2+20x

Factor using the ac-method. - 36x2+21xy+3y236 x ^ { 2 } + 21 x y + 3 y ^ { 2 }36x2+21xy+3y2

Factor. - u2−3uv−18v2u ^ { 2 } - 3 u v - 18 v ^ { 2 }u2−3uv−18v2

Factor using the ac-method. - 15x2+22x+815 x ^ { 2 } + 22 x + 815x2+22x+8

Factor using the ac-method. - x5−2x4−8x3x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 }x5−2x4−8x3

Factor using the ac-method. - 21x2−91x−7021 x ^ { 2 } - 91 x - 7021x2−91x−70

Determine whether the following is a trinomial square. - x2−12x+144x ^ { 2 } - 12 x + 144x2−12x+144

Determine whether the following is a difference of squares. - −81x2+81y2- 81 x ^ { 2 } + 81 y ^ { 2 }−81x2+81y2

Factor. - 4x2−32x+604 x ^ { 2 } - 32 x + 604x2−32x+60

Factor by grouping. - x3−8x2−10x+80x ^ { 3 } - 8 x ^ { 2 } - 10 x + 80x3−8x2−10x+80

Factor completely. - 50a4b−72b350 a ^ { 4 } b - 72 b ^ { 3 }50a4b−72b3

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