Question 1

Factor.
-$a ^ { 6 } - 19 a m ^ { 4 } + 2 a ^ { 3 } m ^ { 5 } - 5 a 6 m m ^ { 4 }$

Accepted Answer

A)  $a m \left( a ^ { 5 } - 19 m ^ { 3 } + 2 a ^ { 2 } m ^ { 4 } - 5 a ^ { 5 } m ^ { 3 } \right)$ 
B)  $a ^ { 2 } \left( a ^ { 5 } - 19 m ^ { 3 } + 2 a ^ { 2 } m ^ { 4 } - 5 a ^ { 5 } m ^ { 3 } \right)$ 
C)  $a \left( a ^ { 5 } - 19 m ^ { 4 } + 2 a ^ { 2 } m ^ { 5 } - 5 a ^ { 5 } m ^ { 4 } \right)$ 
D)  $a m ^ { 4 } \left( a ^ { 5 } - 19 + 2 a ^ { 2 } m ^ { 1 } - 5 a ^ { 5 } \right)$ 
A)  $a m \left( a ^ { 5 } - 19 m ^ { 3 } + 2 a ^ { 2 } m ^ { 4 } - 5 a ^ { 5 } m ^ { 3 } \right)$ 
B)  $a ^ { 2 } \left( a ^ { 5 } - 19 m ^ { 3 } + 2 a ^ { 2 } m ^ { 4 } - 5 a ^ { 5 } m ^ { 3 } \right)$ 
C)  $a \left( a ^ { 5 } - 19 m ^ { 4 } + 2 a ^ { 2 } m ^ { 5 } - 5 a ^ { 5 } m ^ { 4 } \right)$ 
D)  $a m ^ { 4 } \left( a ^ { 5 } - 19 + 2 a ^ { 2 } m ^ { 1 } - 5 a ^ { 5 } \right)$

Question 2

Factor by grouping.
-$$x ^ { 3 } + 3 x ^ { 2 } - 10 x - 30$$

Accepted Answer

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

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

A)  $( 2 x + 4 ) ( x - 3 )$ 
B)  $2 ( x - 2 ) ( x + 3 )$ 
C)  $2 ( x + 2 ) ( x - 3 )$ 
D)  Prime 
A)  $( 2 x + 4 ) ( x - 3 )$ 
B)  $2 ( x - 2 ) ( x + 3 )$ 
C)  $2 ( x + 2 ) ( x - 3 )$ 
D)  Prime

Question 5

Factor.
-$- 30 x ^ { 2 } - 25 x + 30$

Accepted Answer

A)  $5 ( - 3 x + 2 ) ( 2 x + 3 )$ 
B)  $( - 15 x + 10 ) ( 2 x + 3 )$ 
C)  $5 ( 3 x + 2 ) ( - 2 x + 3 )$ 
D)  $( - 3 x + 2 ) ( 10 x + 15 )$ 
A)  $5 ( - 3 x + 2 ) ( 2 x + 3 )$ 
B)  $( - 15 x + 10 ) ( 2 x + 3 )$ 
C)  $5 ( 3 x + 2 ) ( - 2 x + 3 )$ 
D)  $( - 3 x + 2 ) ( 10 x + 15 )$

Question 6

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

Accepted Answer

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

Question 7

Factor.
-$10 x ^ { 4 } - 21 x ^ { 3 } + 9 x ^ { 2 }$

Accepted Answer

A)  $\left( 10 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$ 
B)  $x ( 2 x + 3 ) ( 5 x + 3 )$ 
C)  $x ^ { 2 } ( 2 x - 3 ) ( 5 x - 3 )$ 
D)  $x ^ { 2 } ( 10 x - 1 ) ( x - 9 )$ 
A)  $\left( 10 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$ 
B)  $x ( 2 x + 3 ) ( 5 x + 3 )$ 
C)  $x ^ { 2 } ( 2 x - 3 ) ( 5 x - 3 )$ 
D)  $x ^ { 2 } ( 10 x - 1 ) ( x - 9 )$

Question 8

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

Accepted Answer

A)  $s ( s + 14 )$ 
B)  $( s + 4 ) ( s - 2 )$ 
C)  $( s - 4 ) ( s - 2 )$ 
D)  $( \mathrm { s } + 4 ) ( \mathrm { s } + 2 )$ 
A)  $s ( s + 14 )$ 
B)  $( s + 4 ) ( s - 2 )$ 
C)  $( s - 4 ) ( s - 2 )$ 
D)  $( \mathrm { s } + 4 ) ( \mathrm { s } + 2 )$

Question 9

Factor completely.
-$$x ^ { 10 } + 30 x ^ { 5 } + 225$$

Accepted Answer

A)  $\left( x ^ { 5 } + 15 \right) ^ { 2 }$ 
B)  Prime 
C)  $\left( x ^ { 5 } + 15 \right) \left( x ^ { 5 } - 15 \right)$ 
D)  $\left( x ^ { 5 } - 15 \right) ^ { 2 }$ 
A)  $\left( x ^ { 5 } + 15 \right) ^ { 2 }$ 
B)  Prime 
C)  $\left( x ^ { 5 } + 15 \right) \left( x ^ { 5 } - 15 \right)$ 
D)  $\left( x ^ { 5 } - 15 \right) ^ { 2 }$

Question 10

Determine whether the following is a difference of squares.
-$$144 - y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 11

Factor completely.
-$25 k ^ { 2 } - 169 m ^ { 2 }$

Accepted Answer

A)  $( 5 \mathrm { k } + 13 \mathrm {~m} ) ^ { 2 }$ 
B)  Prime 
C)  $( 5 k - 13 m ) ^ { 2 }$ 
D)  $( 5 k + 13 m ) ( 5 k - 13 m )$ 
A)  $( 5 \mathrm { k } + 13 \mathrm {~m} ) ^ { 2 }$ 
B)  Prime 
C)  $( 5 k - 13 m ) ^ { 2 }$ 
D)  $( 5 k + 13 m ) ( 5 k - 13 m )$

Question 12

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)  $( 4 \mathrm { x } + 3 \mathrm { t } ) ( 4 \mathrm { x } + 3 \mathrm { t } )$ 
D)  Prime 
A)  $( 4 x - 3 t ) ( 4 x - 3 t )$ 
B)  $( 16 x - 3 t ) ( x - 3 t )$ 
C)  $( 4 \mathrm { x } + 3 \mathrm { t } ) ( 4 \mathrm { x } + 3 \mathrm { t } )$ 
D)  Prime

Question 13

Determine whether the following is a difference of squares.
-$$16 x ^ { 2 } - 9 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 14

Factor using the ac-method.
-$$9 x ^ { 4 } + 24 x ^ { 2 } + 16$$

Accepted Answer

A)  $\left( 3 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } + 16 \right)$ 
B)  $\left( 3 x ^ { 2 } + 4 \right) \left( 3 x ^ { 2 } + 4 \right)$ 
C)  $\left( 9 x ^ { 2 } + 4 \right) \left( x ^ { 2 } + 4 \right)$ 
D)  $\left( 3 x ^ { 2 } - 4 \right) \left( 3 x ^ { 2 } - 4 \right)$ 
A)  $\left( 3 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } + 16 \right)$ 
B)  $\left( 3 x ^ { 2 } + 4 \right) \left( 3 x ^ { 2 } + 4 \right)$ 
C)  $\left( 9 x ^ { 2 } + 4 \right) \left( x ^ { 2 } + 4 \right)$ 
D)  $\left( 3 x ^ { 2 } - 4 \right) \left( 3 x ^ { 2 } - 4 \right)$

Question 15

Factor.
-$8 \mathrm { c } ^ { 3 } + 125$

Accepted Answer

A)  $( 2 c + 5 ) \left( 4 c ^ { 2 } - 10 c + 25 \right)$ 
B)  $( 2 c - 5 ) \left( 4 c ^ { 2 } + 10 c + 25 \right)$ 
C)  $( 2 c + 5 ) \left( 4 c ^ { 2 } + 25 \right)$ 
D)  $( 8 c + 5 ) \left( c ^ { 2 } - 10 c + 25 \right)$ 
A)  $( 2 c + 5 ) \left( 4 c ^ { 2 } - 10 c + 25 \right)$ 
B)  $( 2 c - 5 ) \left( 4 c ^ { 2 } + 10 c + 25 \right)$ 
C)  $( 2 c + 5 ) \left( 4 c ^ { 2 } + 25 \right)$ 
D)  $( 8 c + 5 ) \left( c ^ { 2 } - 10 c + 25 \right)$

Question 16

Factor.
-$$3 x ^ { 8 } - 15 x ^ { 7 } + 18 x ^ { 6 }$$

Accepted Answer

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

Question 17

Factor.
-$15 x ^ { 3 } + 29 x ^ { 2 } + 12 x$

Accepted Answer

A)  $\left( 15 x ^ { 2 } + 4 \right) ( x + 3 )$ 
B)  $x ( 15 x + 1 ) ( x + 12 )$ 
C)  $x ( 3 x - 4 ) ( 5 x - 3 )$ 
D)  $x ( 3 x + 4 ) ( 5 x + 3 )$ 
A)  $\left( 15 x ^ { 2 } + 4 \right) ( x + 3 )$ 
B)  $x ( 15 x + 1 ) ( x + 12 )$ 
C)  $x ( 3 x - 4 ) ( 5 x - 3 )$ 
D)  $x ( 3 x + 4 ) ( 5 x + 3 )$

Question 18

Determine whether the following is a difference of squares.
-$$x ^ { 2 } - 25 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 19

Factor.
-$216 p ^ { 3 } - 1$

Accepted Answer

A)  $( 6 p - 1 ) \left( 36 p ^ { 2 } + 1 \right)$ 
B)  $( 6 p + 1 ) \left( 36 p ^ { 2 } - 6 p + 1 \right)$ 
C)  $( 216 p - 1 ) \left( p ^ { 2 } + 6 p + 1 \right)$ 
D)  $( 6 p - 1 ) \left( 36 p ^ { 2 } + 6 p + 1 \right)$ 
A)  $( 6 p - 1 ) \left( 36 p ^ { 2 } + 1 \right)$ 
B)  $( 6 p + 1 ) \left( 36 p ^ { 2 } - 6 p + 1 \right)$ 
C)  $( 216 p - 1 ) \left( p ^ { 2 } + 6 p + 1 \right)$ 
D)  $( 6 p - 1 ) \left( 36 p ^ { 2 } + 6 p + 1 \right)$

Question 20

Factor completely.
-$$x ^ { 2 } + 2 x y - 35 y ^ { 2 }$$

Accepted Answer

A)  $( x - 7 y ) ( x + y )$ 
B)  $( x - 7 y ) ( x + 5 y )$ 
C)  $( x - y ) ( x + 5 y )$ 
D)  $( x + 7 y ) ( x - 5 y )$ 
A)  $( x - 7 y ) ( x + y )$ 
B)  $( x - 7 y ) ( x + 5 y )$ 
C)  $( x - y ) ( x + 5 y )$ 
D)  $( x + 7 y ) ( x - 5 y )$

Factor. - $a ^ { 6 } - 19 a m ^ { 4 } + 2 a ^ { 3 } m ^ { 5 } - 5 a 6 m m ^ { 4 }$

Factor by grouping. - $x ^ { 3 } + 3 x ^ { 2 } - 10 x - 30$

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

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

Factor. - $- 30 x ^ { 2 } - 25 x + 30$

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

Factor. - $10 x ^ { 4 } - 21 x ^ { 3 } + 9 x ^ { 2 }$

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

Factor completely. - $x ^ { 10 } + 30 x ^ { 5 } + 225$

Determine whether the following is a difference of squares. - $144 - y ^ { 2 }$

Factor completely. - $25 k ^ { 2 } - 169 m ^ { 2 }$

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

Determine whether the following is a difference of squares. - $16 x ^ { 2 } - 9 y ^ { 2 }$

Factor using the ac-method. - $9 x ^ { 4 } + 24 x ^ { 2 } + 16$

Factor. - $8 \mathrm { c } ^ { 3 } + 125$

Factor. - $3 x ^ { 8 } - 15 x ^ { 7 } + 18 x ^ { 6 }$

Factor. - $15 x ^ { 3 } + 29 x ^ { 2 } + 12 x$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 25 y ^ { 2 }$

Factor. - $216 p ^ { 3 } - 1$

Factor completely. - $x ^ { 2 } + 2 x y - 35 y ^ { 2 }$

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

Filters

Exam 5: Polynomials: Factoring

Factor. - a6−19am4+2a3m5−5a6mm4a ^ { 6 } - 19 a m ^ { 4 } + 2 a ^ { 3 } m ^ { 5 } - 5 a 6 m m ^ { 4 }a6−19am4+2a3m5−5a6mm4

Factor by grouping. - x3+3x2−10x−30x ^ { 3 } + 3 x ^ { 2 } - 10 x - 30x3+3x2−10x−30

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

Factor. - 2x2−2x−122 x ^ { 2 } - 2 x - 122x2−2x−12

Factor. - −30x2−25x+30- 30 x ^ { 2 } - 25 x + 30−30x2−25x+30

Factor completely. - 25x2−20x+425 x ^ { 2 } - 20 x + 425x2−20x+4

Factor. - 10x4−21x3+9x210 x ^ { 4 } - 21 x ^ { 3 } + 9 x ^ { 2 }10x4−21x3+9x2

Factor by grouping. - s2+4s+2s+8s ^ { 2 } + 4 s + 2 s + 8s2+4s+2s+8

Factor completely. - x10+30x5+225x ^ { 10 } + 30 x ^ { 5 } + 225x10+30x5+225

Determine whether the following is a difference of squares. - 144−y2144 - y ^ { 2 }144−y2

Factor completely. - 25k2−169m225 k ^ { 2 } - 169 m ^ { 2 }25k2−169m2

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

Determine whether the following is a difference of squares. - 16x2−9y216 x ^ { 2 } - 9 y ^ { 2 }16x2−9y2

Factor using the ac-method. - 9x4+24x2+169 x ^ { 4 } + 24 x ^ { 2 } + 169x4+24x2+16

Factor. - 8c3+1258 \mathrm { c } ^ { 3 } + 1258c3+125

Factor. - 3x8−15x7+18x63 x ^ { 8 } - 15 x ^ { 7 } + 18 x ^ { 6 }3x8−15x7+18x6

Factor. - 15x3+29x2+12x15 x ^ { 3 } + 29 x ^ { 2 } + 12 x15x3+29x2+12x

Determine whether the following is a difference of squares. - x2−25y2x ^ { 2 } - 25 y ^ { 2 }x2−25y2

Factor. - 216p3−1216 p ^ { 3 } - 1216p3−1

Factor completely. - x2+2xy−35y2x ^ { 2 } + 2 x y - 35 y ^ { 2 }x2+2xy−35y2

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. - $a ^ { 6 } - 19 a m ^ { 4 } + 2 a ^ { 3 } m ^ { 5 } - 5 a 6 m m ^ { 4 }$

Factor by grouping. - $x ^ { 3 } + 3 x ^ { 2 } - 10 x - 30$

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

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

Factor. - $- 30 x ^ { 2 } - 25 x + 30$

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

Factor. - $10 x ^ { 4 } - 21 x ^ { 3 } + 9 x ^ { 2 }$

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

Factor completely. - $x ^ { 10 } + 30 x ^ { 5 } + 225$

Determine whether the following is a difference of squares. - $144 - y ^ { 2 }$

Factor completely. - $25 k ^ { 2 } - 169 m ^ { 2 }$

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

Determine whether the following is a difference of squares. - $16 x ^ { 2 } - 9 y ^ { 2 }$

Factor using the ac-method. - $9 x ^ { 4 } + 24 x ^ { 2 } + 16$

Factor. - $8 \mathrm { c } ^ { 3 } + 125$

Factor. - $3 x ^ { 8 } - 15 x ^ { 7 } + 18 x ^ { 6 }$

Factor. - $15 x ^ { 3 } + 29 x ^ { 2 } + 12 x$

Determine whether the following is a difference of squares. - $x ^ { 2 } - 25 y ^ { 2 }$

Factor. - $216 p ^ { 3 } - 1$

Factor completely. - $x ^ { 2 } + 2 x y - 35 y ^ { 2 }$