Question 1

Factor.
-$15 z ^ { 4 } - 8 z ^ { 2 } - 16$

Accepted Answer

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

Question 2

Factor completely.
-$$8 x ^ { 2 } - 18$$

Accepted Answer

A)  $2 ( 2 x - 3 ) ^ { 2 }$ 
B)  $2 ( 2 x + 3 ) ( 2 x - 3 )$ 
C)  $( 2 x + 3 ) ( 4 x - 6 )$ 
D)  $( 4 x + 6 ) ( 2 x - 3 )$ 
A)  $2 ( 2 x - 3 ) ^ { 2 }$ 
B)  $2 ( 2 x + 3 ) ( 2 x - 3 )$ 
C)  $( 2 x + 3 ) ( 4 x - 6 )$ 
D)  $( 4 x + 6 ) ( 2 x - 3 )$ B

Question 3

Factor completely.
-$121 \mathrm { k } ^ { 2 } - 100 \mathrm {~m} ^ { 2 }$

Accepted Answer

A)  $( 11 \mathrm { k } + 10 \mathrm {~m} ) ( 11 \mathrm { k } - 10 \mathrm {~m} )$ 
B)  $( 11 \mathrm { k } + 10 \mathrm {~m} ) ^ { 2 }$ 
C)  $( 11 \mathrm { k } - 10 \mathrm {~m} ) ^ { 2 }$ 
D)  $( 121 \mathrm { k } + \mathrm { m } ) ( \mathrm { k } - 100 \mathrm {~m} )$ 
A)  $( 11 \mathrm { k } + 10 \mathrm {~m} ) ( 11 \mathrm { k } - 10 \mathrm {~m} )$ 
B)  $( 11 \mathrm { k } + 10 \mathrm {~m} ) ^ { 2 }$ 
C)  $( 11 \mathrm { k } - 10 \mathrm {~m} ) ^ { 2 }$ 
D)  $( 121 \mathrm { k } + \mathrm { m } ) ( \mathrm { k } - 100 \mathrm {~m} )$ A

Question 4

Factor completely.
-$3 x ^ { 8 } - 768$

Accepted Answer

A)  $3 \left( x ^ { 4 } + 16 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
B)  $3 \left( x ^ { 4 } - 16 \right) ^ { 2 }$ 
C)  $\left( 3 x ^ { 4 } + 48 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
D)  $3 \left( x ^ { 4 } + 16 \right) \left( x ^ { 4 } - 16 \right)$ 
A)  $3 \left( x ^ { 4 } + 16 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
B)  $3 \left( x ^ { 4 } - 16 \right) ^ { 2 }$ 
C)  $\left( 3 x ^ { 4 } + 48 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
D)  $3 \left( x ^ { 4 } + 16 \right) \left( x ^ { 4 } - 16 \right)$

Question 5

Factor completely.
-$$a ^ { 2 } - 40 a b + 400 b ^ { 2 }$$

Accepted Answer

A)  $( a - 20 b ) ^ { 2 }$ 
B)  $( a + 20 b ) ( a - 20 b )$ 
C)  $( a + 20 b ) ^ { 2 }$ 
D)  Prime 
A)  $( a - 20 b ) ^ { 2 }$ 
B)  $( a + 20 b ) ( a - 20 b )$ 
C)  $( a + 20 b ) ^ { 2 }$ 
D)  Prime

Question 6

Factor.
-$p ^ { 4 } - 11 p ^ { 2 } + 24$

Accepted Answer

A)  $p ^ { 2 } ( p - 8 ) ( p - 3 )$ 
B)  $\left( p ^ { 2 } - 24 \right) \left( p ^ { 2 } - 1 \right)$ 
C)  $\left( p ^ { 2 } - 8 \right) \left( p ^ { 2 } - 3 \right)$ 
D)  $\left( p ^ { 2 } - 8 \right) \left( p ^ { 2 } + 3 \right)$ 
A)  $p ^ { 2 } ( p - 8 ) ( p - 3 )$ 
B)  $\left( p ^ { 2 } - 24 \right) \left( p ^ { 2 } - 1 \right)$ 
C)  $\left( p ^ { 2 } - 8 \right) \left( p ^ { 2 } - 3 \right)$ 
D)  $\left( p ^ { 2 } - 8 \right) \left( p ^ { 2 } + 3 \right)$

Question 7

Factor.
-$375 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }$

Accepted Answer

A)  $3 \mathrm {~m} \left( 5 \mathrm { k } + 4 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } - 20 \mathrm {~km} + 16 \mathrm {~km} ^ { 2 } \right)$ 
B)  $3 \mathrm {~m} ( 125 \mathrm { k } - 4 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$ 
C)  $\left( 15 k m - 12 m ^ { 2 } \right) \left( 25 k ^ { 2 } + 16 m ^ { 2 } \right)$ 
D)  $3 m ( 5 k - 4 m ) \left( 25 k ^ { 2 } + 20 k m + 16 m ^ { 2 } \right)$ 
A)  $3 \mathrm {~m} \left( 5 \mathrm { k } + 4 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } - 20 \mathrm {~km} + 16 \mathrm {~km} ^ { 2 } \right)$ 
B)  $3 \mathrm {~m} ( 125 \mathrm { k } - 4 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$ 
C)  $\left( 15 k m - 12 m ^ { 2 } \right) \left( 25 k ^ { 2 } + 16 m ^ { 2 } \right)$ 
D)  $3 m ( 5 k - 4 m ) \left( 25 k ^ { 2 } + 20 k m + 16 m ^ { 2 } \right)$

Question 8

Factor.
-$$x ^ { 2 } + 7 x y - 120 y ^ { 2 }$$

Accepted Answer

A)  $( x + 15 y ) ( x - 8 y )$ 
B)  $( x - y ) ( x + 8 y )$ 
C)  $( x - 15 y ) ( x + y )$ 
D)  $( x - 15 y ) ( x + 8 y )$ 
A)  $( x + 15 y ) ( x - 8 y )$ 
B)  $( x - y ) ( x + 8 y )$ 
C)  $( x - 15 y ) ( x + y )$ 
D)  $( x - 15 y ) ( x + 8 y )$

Question 9

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

Accepted Answer

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

Question 10

Factor.
-$40 x ^ { 8 } y ^ { 9 } + 64 x ^ { 6 } y ^ { 5 } + 80 x ^ { 4 } y ^ { 2 }$

Accepted Answer

A)  No common factor 
B)  $8 \left( 5 x ^ { 8 } y ^ { 9 } + 8 x ^ { 6 } y ^ { 5 } + 10 x ^ { 4 } y ^ { 2 } \right)$ 
C)  $8 x ^ { 4 } \left( 5 x ^ { 4 } y ^ { 9 } + 8 x ^ { 2 } y ^ { 5 } + 10 y ^ { 2 } \right)$ 
D)  $8 x ^ { 4 } y ^ { 2 } \left( 5 x ^ { 4 } y ^ { 7 } + 8 x ^ { 2 } y ^ { 3 } + 10 \right)$ 
A)  No common factor 
B)  $8 \left( 5 x ^ { 8 } y ^ { 9 } + 8 x ^ { 6 } y ^ { 5 } + 10 x ^ { 4 } y ^ { 2 } \right)$ 
C)  $8 x ^ { 4 } \left( 5 x ^ { 4 } y ^ { 9 } + 8 x ^ { 2 } y ^ { 5 } + 10 y ^ { 2 } \right)$ 
D)  $8 x ^ { 4 } y ^ { 2 } \left( 5 x ^ { 4 } y ^ { 7 } + 8 x ^ { 2 } y ^ { 3 } + 10 \right)$

Question 11

Factor by grouping.
-$$x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8$$

Accepted Answer

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

Question 12

Factor using the ac-method.
-$$84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$$

Accepted Answer

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

Question 13

Factor.
-$5 x ^ { 9 } - 40 x ^ { 8 } - 60 x ^ { 7 }$

Accepted Answer

A)  $5 x ^ { 7 } \left( x ^ { 2 } - 6 x - 12 \right)$ 
B)  $5 x ^ { 7 } ( x - 6 ) ( x - 2 )$ 
C)  $5 x ^ { 7 } ( x - 6 ) ( x + 2 )$ 
D)  $5 x ^ { 6 } \left( x ^ { 2 } - 6 x - 12 \right)$ 
A)  $5 x ^ { 7 } \left( x ^ { 2 } - 6 x - 12 \right)$ 
B)  $5 x ^ { 7 } ( x - 6 ) ( x - 2 )$ 
C)  $5 x ^ { 7 } ( x - 6 ) ( x + 2 )$ 
D)  $5 x ^ { 6 } \left( x ^ { 2 } - 6 x - 12 \right)$

Question 14

Factor.
-$16 x ^ { 2 } - 24 x t + 9 t ^ { 2 }$

Accepted Answer

A)  $( 4 x + 3 t ) ( 4 x + 3 t )$ 
B)  $( 16 x - 3 t ) ( x - 3 t )$ 
C)  Prime 
D)  $( 4 x - 3 t ) ( 4 x - 3 t )$ 
A)  $( 4 x + 3 t ) ( 4 x + 3 t )$ 
B)  $( 16 x - 3 t ) ( x - 3 t )$ 
C)  Prime 
D)  $( 4 x - 3 t ) ( 4 x - 3 t )$

Question 15

Factor completely.
-$$9 m ^ { 2 } - \frac { 4 } { 9 }$$

Accepted Answer

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

Question 16

Factor.
-$$\mathrm { t } ( 2 - \mathrm { m } ) + \mathrm { s } ( 2 - \mathrm { m } )$$

Accepted Answer

A)  No common factor 
B)  $( t - s ) ( 2 - m )$ 
C)  $\mathrm { t } ( 2 - \mathrm { m } ) + \mathrm { s }$ 
D)  $( t + s ) ( 2 - m )$ 
A)  No common factor 
B)  $( t - s ) ( 2 - m )$ 
C)  $\mathrm { t } ( 2 - \mathrm { m } ) + \mathrm { s }$ 
D)  $( t + s ) ( 2 - m )$

Question 17

Factor.
-$$6 y ^ { 2 } + 27 y - 15$$

Accepted Answer

A)  $3 ( 2 y + 1 ) ( y - 5 )$ 
B)  $3 ( 2 y - 1 ) ( y + 5 )$ 
C)  $( 2 y - 1 ) ( 3 y + 15 )$ 
D)  $( 6 y - 3 ) ( y + 5 )$ 
A)  $3 ( 2 y + 1 ) ( y - 5 )$ 
B)  $3 ( 2 y - 1 ) ( y + 5 )$ 
C)  $( 2 y - 1 ) ( 3 y + 15 )$ 
D)  $( 6 y - 3 ) ( y + 5 )$

Question 18

Factor by grouping.
-$$s ^ { 2 } + 4 s + 9 s + 36$$

Accepted Answer

A)  $( \mathrm { s } + 4 ) ( \mathrm { s } - 9 )$ 
B)  $s ( s + 49 )$ 
C)  $( s - 4 ) ( s - 9 )$ 
D)  $( s + 4 ) ( s + 9 )$ 
A)  $( \mathrm { s } + 4 ) ( \mathrm { s } - 9 )$ 
B)  $s ( s + 49 )$ 
C)  $( s - 4 ) ( s - 9 )$ 
D)  $( s + 4 ) ( s + 9 )$

Question 19

Find the GCF.
-$$- x ^ { 2 } , - 2 x , - 4 x ^ { 5 }$$

Accepted Answer

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

Question 20

Factor completely.
-$$u ^ { 2 } - 4 u v - 32 v ^ { 2 }$$

Accepted Answer

A)  $( u + 4 v ) ( u - 8 v )$ 
B)  $( u - 4 v ) ( u + v )$ 
C)  $( u - v ) ( u + 8 v )$ 
D)  $( u - 4 v ) ( u + 8 v )$ 
A)  $( u + 4 v ) ( u - 8 v )$ 
B)  $( u - 4 v ) ( u + v )$ 
C)  $( u - v ) ( u + 8 v )$ 
D)  $( u - 4 v ) ( u + 8 v )$

Factor. - $15 z ^ { 4 } - 8 z ^ { 2 } - 16$

Factor completely. - $8 x ^ { 2 } - 18$

Factor completely. - $121 \mathrm { k } ^ { 2 } - 100 \mathrm {~m} ^ { 2 }$

Factor completely. - $3 x ^ { 8 } - 768$

Factor completely. - $a ^ { 2 } - 40 a b + 400 b ^ { 2 }$

Factor. - $p ^ { 4 } - 11 p ^ { 2 } + 24$

Factor. - $375 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }$

Factor. - $x ^ { 2 } + 7 x y - 120 y ^ { 2 }$

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

Factor. - $40 x ^ { 8 } y ^ { 9 } + 64 x ^ { 6 } y ^ { 5 } + 80 x ^ { 4 } y ^ { 2 }$

Factor by grouping. - $x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8$

Factor using the ac-method. - $84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$

Factor. - $5 x ^ { 9 } - 40 x ^ { 8 } - 60 x ^ { 7 }$

Factor. - $16 x ^ { 2 } - 24 x t + 9 t ^ { 2 }$

Factor completely. - $9 m ^ { 2 } - \frac { 4 } { 9 }$

Factor. - $\mathrm { t } ( 2 - \mathrm { m } ) + \mathrm { s } ( 2 - \mathrm { m } )$

Factor. - $6 y ^ { 2 } + 27 y - 15$

Factor by grouping. - $s ^ { 2 } + 4 s + 9 s + 36$

Find the GCF. - $- x ^ { 2 } , - 2 x , - 4 x ^ { 5 }$

Factor completely. - $u ^ { 2 } - 4 u v - 32 v ^ { 2 }$

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. - 15z4−8z2−1615 z ^ { 4 } - 8 z ^ { 2 } - 1615z4−8z2−16

Factor completely. - 8x2−188 x ^ { 2 } - 188x2−18

Factor completely. - 121k2−100 m2121 \mathrm { k } ^ { 2 } - 100 \mathrm {~m} ^ { 2 }121k2−100 m2

Factor completely. - 3x8−7683 x ^ { 8 } - 7683x8−768

Factor completely. - a2−40ab+400b2a ^ { 2 } - 40 a b + 400 b ^ { 2 }a2−40ab+400b2

Factor. - p4−11p2+24p ^ { 4 } - 11 p ^ { 2 } + 24p4−11p2+24

Factor. - 375k3 m−192 m4375 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }375k3 m−192 m4

Factor. - x2+7xy−120y2x ^ { 2 } + 7 x y - 120 y ^ { 2 }x2+7xy−120y2

Factor. - x2+23x+19x ^ { 2 } + \frac { 2 } { 3 } x + \frac { 1 } { 9 }x2+32​x+91​

Factor. - 40x8y9+64x6y5+80x4y240 x ^ { 8 } y ^ { 9 } + 64 x ^ { 6 } y ^ { 5 } + 80 x ^ { 4 } y ^ { 2 }40x8y9+64x6y5+80x4y2

Factor by grouping. - x3−2x2+4x−8x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8x3−2x2+4x−8

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

Factor. - 5x9−40x8−60x75 x ^ { 9 } - 40 x ^ { 8 } - 60 x ^ { 7 }5x9−40x8−60x7

Factor. - 16x2−24xt+9t216 x ^ { 2 } - 24 x t + 9 t ^ { 2 }16x2−24xt+9t2

Factor completely. - 9m2−499 m ^ { 2 } - \frac { 4 } { 9 }9m2−94​

Factor. - t(2−m)+s(2−m)\mathrm { t } ( 2 - \mathrm { m } ) + \mathrm { s } ( 2 - \mathrm { m } )t(2−m)+s(2−m)

Factor. - 6y2+27y−156 y ^ { 2 } + 27 y - 156y2+27y−15

Factor by grouping. - s2+4s+9s+36s ^ { 2 } + 4 s + 9 s + 36s2+4s+9s+36

Find the GCF. - −x2,−2x,−4x5- x ^ { 2 } , - 2 x , - 4 x ^ { 5 }−x2,−2x,−4x5

Factor completely. - u2−4uv−32v2u ^ { 2 } - 4 u v - 32 v ^ { 2 }u2−4uv−32v2