Question 1

Factor using the ac-method.
-$18 - 9 x + x ^ { 2 }$

Accepted Answer

A)  $( x - 6 ) ( x - 3 )$ 
B)  $( x + 6 ) ( x - 3 )$ 
C)  $( x + 6 ) ( x + 3 )$ 
D)  $( x - 6 ) ( x + 3 )$ 
A)  $( x - 6 ) ( x - 3 )$ 
B)  $( x + 6 ) ( x - 3 )$ 
C)  $( x + 6 ) ( x + 3 )$ 
D)  $( x - 6 ) ( x + 3 )$ A

Question 2

Factor by grouping.
-$$x ^ { 3 } + 6 x ^ { 2 } + 8 x + 48$$

Accepted Answer

A)  $( x + 6 ) \left( x ^ { 2 } + 8 \right)$ 
B)  $( x + 6 ) \left( x ^ { 2 } - 8 \right)$ 
C)  $( x - 6 ) \left( x ^ { 3 } + 8 \right)$ 
D)  $( x + 6 x ) \left( x ^ { 2 } + 8 \right)$ 
A)  $( x + 6 ) \left( x ^ { 2 } + 8 \right)$ 
B)  $( x + 6 ) \left( x ^ { 2 } - 8 \right)$ 
C)  $( x - 6 ) \left( x ^ { 3 } + 8 \right)$ 
D)  $( x + 6 x ) \left( x ^ { 2 } + 8 \right)$ A

Question 3

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

Accepted Answer

A) True 
 B)False   True

Question 4

Factor completely.
-$25 x - 16 x ^ { 3 }$

Accepted Answer

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

Question 5

Factor.
-$90 x ^ { 6 } y ^ { 6 } + 18 x ^ { 4 } y ^ { 4 } + 27 x ^ { 2 } y ^ { 2 }$

Accepted Answer

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

Question 6

Factor.
-$$t ( 7 - m ) + s ( 7 - m )$$

Accepted Answer

A)  No common factor 
B)  $( t - s ) ( 7 - m )$ 
C)  $( \mathrm { t } + \mathrm { s } ) ( 7 - \mathrm { m } )$ 
D)  $t ( 7 - m ) + s$ 
A)  No common factor 
B)  $( t - s ) ( 7 - m )$ 
C)  $( \mathrm { t } + \mathrm { s } ) ( 7 - \mathrm { m } )$ 
D)  $t ( 7 - m ) + s$

Question 7

Factor using the ac-method.
-$- 30 x ^ { 2 } - 25 x + 30$

Accepted Answer

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

Question 8

Factor.
-$0.064 r ^ { 3 } - 0.027 s ^ { 3 }$

Accepted Answer

A)  $( 0.4 r + 0.3 s ) \left( 0.16 r ^ { 2 } - 0.12 r s - 0.09 s ^ { 2 } \right)$ 
B)  $( 0.4 \mathrm { r } - 0.3 \mathrm {~s} ) \left( 0.16 \mathrm { r } ^ { 2 } + 0.12 \mathrm { rs } + 0.09 \mathrm {~s} ^ { 2 } \right)$ 
C)  $( 0.4 \mathrm { r } - \mathrm { s } ) \left( 0.048 \mathrm { r } ^ { 2 } + 0.4 \mathrm { rs } + 0.036 \mathrm {~s} ^ { 2 } \right)$ 
D)  $( 0.4 \mathrm { r } + \mathrm { s } ) \left( 0.048 \mathrm { r } ^ { 2 } - 0.4 \mathrm { rs } - 0.036 \mathrm {~s} ^ { 2 } \right)$ 
A)  $( 0.4 r + 0.3 s ) \left( 0.16 r ^ { 2 } - 0.12 r s - 0.09 s ^ { 2 } \right)$ 
B)  $( 0.4 \mathrm { r } - 0.3 \mathrm {~s} ) \left( 0.16 \mathrm { r } ^ { 2 } + 0.12 \mathrm { rs } + 0.09 \mathrm {~s} ^ { 2 } \right)$ 
C)  $( 0.4 \mathrm { r } - \mathrm { s } ) \left( 0.048 \mathrm { r } ^ { 2 } + 0.4 \mathrm { rs } + 0.036 \mathrm {~s} ^ { 2 } \right)$ 
D)  $( 0.4 \mathrm { r } + \mathrm { s } ) \left( 0.048 \mathrm { r } ^ { 2 } - 0.4 \mathrm { rs } - 0.036 \mathrm {~s} ^ { 2 } \right)$

Question 9

Factor completely.
-$25 x ^ { 2 } - 36$

Accepted Answer

A)  $( 5 x - 6 ) ^ { 2 }$ 
B)  $( 25 x + 1 ) ( x - 36 )$ 
C)  $( 5 x + 6 ) ( 5 x - 6 )$ 
D)  $( 5 x + 6 ) ^ { 2 }$ 
A)  $( 5 x - 6 ) ^ { 2 }$ 
B)  $( 25 x + 1 ) ( x - 36 )$ 
C)  $( 5 x + 6 ) ( 5 x - 6 )$ 
D)  $( 5 x + 6 ) ^ { 2 }$

Question 10

Factor.
-$\mathrm { x } ^ { 3 } - 125$

Accepted Answer

A)  $( x - 5 ) \left( x ^ { 2 } + 5 x + 25 \right)$ 
B)  $( x + 5 ) \left( x ^ { 2 } - 5 x + 25 \right)$ 
C)  $( x + 125 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x - 5 ) \left( x ^ { 2 } + 25 \right)$ 
A)  $( x - 5 ) \left( x ^ { 2 } + 5 x + 25 \right)$ 
B)  $( x + 5 ) \left( x ^ { 2 } - 5 x + 25 \right)$ 
C)  $( x + 125 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x - 5 ) \left( x ^ { 2 } + 25 \right)$

Question 11

Factor completely.
-$$y ^ { 2 } - 100$$

Accepted Answer

A)  $( y + 100 ) ( y - 100 )$ 
B)  $( y + 10 ) ( y - 10 )$ 
C)  $( \mathrm { y } - 10 ) ( \mathrm { y } - 10 )$ 
D)  $\left( y ^ { 2 } + 10 \right) \left( y ^ { 2 } - 10 \right)$ 
A)  $( y + 100 ) ( y - 100 )$ 
B)  $( y + 10 ) ( y - 10 )$ 
C)  $( \mathrm { y } - 10 ) ( \mathrm { y } - 10 )$ 
D)  $\left( y ^ { 2 } + 10 \right) \left( y ^ { 2 } - 10 \right)$

Question 12

Factor.
-$$5 x ^ { 8 } - 60 x ^ { 7 } - 175 x ^ { 6 }$$

Accepted Answer

A)  $5 x ^ { 6 } \left( x ^ { 2 } - 4 x - 35 \right)$ 
B)  $5 x ^ { 5 } \left( x ^ { 2 } - 4 x - 35 \right)$ 
C)  $5 x ^ { 6 } ( x - 7 ) ( x - 5 )$ 
D)  $5 x ^ { 6 } ( x - 7 ) ( x + 5 )$ 
A)  $5 x ^ { 6 } \left( x ^ { 2 } - 4 x - 35 \right)$ 
B)  $5 x ^ { 5 } \left( x ^ { 2 } - 4 x - 35 \right)$ 
C)  $5 x ^ { 6 } ( x - 7 ) ( x - 5 )$ 
D)  $5 x ^ { 6 } ( x - 7 ) ( x + 5 )$

Question 13

Factor.
-$$y ^ { 6 } + 1$$

Accepted Answer

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

Question 14

Factor using the ac-method.
-$6 y ^ { 4 } + 5 y ^ { 2 } - 6$

Accepted Answer

A)  $\left( 6 y ^ { 2 } - 2 \right) \left( y ^ { 2 } + 3 \right)$ 
B)  $\left( 3 y ^ { 2 } + 1 \right) \left( 2 y ^ { 2 } - 6 \right)$ 
C)  $( 2 y - 3 ) ( 3 y + 2 )$ 
D)  $\left( 3 y ^ { 2 } - 2 \right) \left( 2 y ^ { 2 } + 3 \right)$ 
A)  $\left( 6 y ^ { 2 } - 2 \right) \left( y ^ { 2 } + 3 \right)$ 
B)  $\left( 3 y ^ { 2 } + 1 \right) \left( 2 y ^ { 2 } - 6 \right)$ 
C)  $( 2 y - 3 ) ( 3 y + 2 )$ 
D)  $\left( 3 y ^ { 2 } - 2 \right) \left( 2 y ^ { 2 } + 3 \right)$

Question 15

Factor completely.
-$$36 + 12 x + x ^ { 2 }$$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Factor.
-$$x ^ { 3 } + 9 x ^ { 2 } - 36 x$$

Accepted Answer

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

Question 18

Factor.
-$x ^ { 2 } - 3 x y - 10 y ^ { 2 }$

Accepted Answer

A)  $( x - y ) ( x + 2 y )$ 
B)  $( x + 5 y ) ( x - 2 y )$ 
C)  $( x - 5 y ) ( x + y )$ 
D)  $( x - 5 y ) ( x + 2 y )$ 
A)  $( x - y ) ( x + 2 y )$ 
B)  $( x + 5 y ) ( x - 2 y )$ 
C)  $( x - 5 y ) ( x + y )$ 
D)  $( x - 5 y ) ( x + 2 y )$

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

A)  $( t + 0.9 ) ( t + 0.14 )$ 
B)  $( t + 0.45 ) ^ { 2 }$ 
C)  $( t + 0.7 ) ( t + 0.2 )$ 
D)  Prime 
A)  $( t + 0.9 ) ( t + 0.14 )$ 
B)  $( t + 0.45 ) ^ { 2 }$ 
C)  $( t + 0.7 ) ( t + 0.2 )$ 
D)  Prime

Factor using the ac-method. - $18 - 9 x + x ^ { 2 }$

Factor by grouping. - $x ^ { 3 } + 6 x ^ { 2 } + 8 x + 48$

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

Factor completely. - $25 x - 16 x ^ { 3 }$

Factor. - $90 x ^ { 6 } y ^ { 6 } + 18 x ^ { 4 } y ^ { 4 } + 27 x ^ { 2 } y ^ { 2 }$

Factor. - $t ( 7 - m ) + s ( 7 - m )$

Factor using the ac-method. - $- 30 x ^ { 2 } - 25 x + 30$

Factor. - $0.064 r ^ { 3 } - 0.027 s ^ { 3 }$

Factor completely. - $25 x ^ { 2 } - 36$

Factor. - $\mathrm { x } ^ { 3 } - 125$

Factor completely. - $y ^ { 2 } - 100$

Factor. - $5 x ^ { 8 } - 60 x ^ { 7 } - 175 x ^ { 6 }$

Factor. - $y ^ { 6 } + 1$

Factor using the ac-method. - $6 y ^ { 4 } + 5 y ^ { 2 } - 6$

Factor completely. - $36 + 12 x + x ^ { 2 }$

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

Factor. - $x ^ { 3 } + 9 x ^ { 2 } - 36 x$

Factor. - $x ^ { 2 } - 3 x y - 10 y ^ { 2 }$

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

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

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 using the ac-method. - 18−9x+x218 - 9 x + x ^ { 2 }18−9x+x2

Factor by grouping. - x3+6x2+8x+48x ^ { 3 } + 6 x ^ { 2 } + 8 x + 48x3+6x2+8x+48

Determine whether the following is a trinomial square. - x2+12xy+36y2x ^ { 2 } + 12 x y + 36 y ^ { 2 }x2+12xy+36y2

Factor completely. - 25x−16x325 x - 16 x ^ { 3 }25x−16x3

Factor. - 90x6y6+18x4y4+27x2y290 x ^ { 6 } y ^ { 6 } + 18 x ^ { 4 } y ^ { 4 } + 27 x ^ { 2 } y ^ { 2 }90x6y6+18x4y4+27x2y2

Factor. - t(7−m)+s(7−m)t ( 7 - m ) + s ( 7 - m )t(7−m)+s(7−m)

Factor using the ac-method. - −30x2−25x+30- 30 x ^ { 2 } - 25 x + 30−30x2−25x+30

Factor. - 0.064r3−0.027s30.064 r ^ { 3 } - 0.027 s ^ { 3 }0.064r3−0.027s3

Factor completely. - 25x2−3625 x ^ { 2 } - 3625x2−36

Factor. - x3−125\mathrm { x } ^ { 3 } - 125x3−125

Factor completely. - y2−100y ^ { 2 } - 100y2−100

Factor. - 5x8−60x7−175x65 x ^ { 8 } - 60 x ^ { 7 } - 175 x ^ { 6 }5x8−60x7−175x6

Factor. - y6+1y ^ { 6 } + 1y6+1

Factor using the ac-method. - 6y4+5y2−66 y ^ { 4 } + 5 y ^ { 2 } - 66y4+5y2−6

Factor completely. - 36+12x+x236 + 12 x + x ^ { 2 }36+12x+x2

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

Factor. - x3+9x2−36xx ^ { 3 } + 9 x ^ { 2 } - 36 xx3+9x2−36x

Factor. - x2−3xy−10y2x ^ { 2 } - 3 x y - 10 y ^ { 2 }x2−3xy−10y2

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

Factor. - t2+0.9t+0.14t ^ { 2 } + 0.9 t + 0.14t2+0.9t+0.14