Question 1

Factor completely.
-$49 x - 16 x ^ { 3 }$

Accepted Answer

A)  $x ( 7 + 4 x ) ( 7 - 4 x )$ 
B)  prime 
C)  $x ( 7 + 4 x ) ^ { 2 }$ 
D)  $x ( 7 - 4 x ) ( 7 - 4 x )$ 
A)  $x ( 7 + 4 x ) ( 7 - 4 x )$ 
B)  prime 
C)  $x ( 7 + 4 x ) ^ { 2 }$ 
D)  $x ( 7 - 4 x ) ( 7 - 4 x )$

Question 2

Factor.
-$3 x ^ { 2 } y ^ { 6 } + 6 x ^ { 2 } y ^ { 5 }$

Accepted Answer

A)  $3 x ^ { 2 } y ^ { 5 } ( y + 2 )$ 
B)  $3 x ^ { 5 } y ^ { 2 } ( y + 2 )$ 
C)  $y + 2$ 
D)  $x ^ { 2 } y ^ { 5 } ( 3 y + 2 )$ 
A)  $3 x ^ { 2 } y ^ { 5 } ( y + 2 )$ 
B)  $3 x ^ { 5 } y ^ { 2 } ( y + 2 )$ 
C)  $y + 2$ 
D)  $x ^ { 2 } y ^ { 5 } ( 3 y + 2 )$

Question 3

Factor.
-$u ^ { 2 } - 2 u v - 15 v ^ { 2 }$

Accepted Answer

A)  $( u + 3 v ) ( u - 5 v )$ 
B)  $( u - 3 v ) ( u + v )$ 
C)  $( u - 3 v ) ( u + 5 v )$ 
D)  $( u - v ) ( u + 5 v )$ 
A)  $( u + 3 v ) ( u - 5 v )$ 
B)  $( u - 3 v ) ( u + v )$ 
C)  $( u - 3 v ) ( u + 5 v )$ 
D)  $( u - v ) ( u + 5 v )$

Question 4

Factor.
-$$8 x ^ { 2 } - 24 x y - 32 y ^ { 2 }$$

Accepted Answer

A)  $8 ( x - y ) ( x + 4 y )$ 
B)  $( 8 x - 8 y ) ( x + 4 y )$ 
C)  $( x - y ) ( 8 x + 24 y )$ 
D)  $8 ( x + y ) ( x - 4 y )$ 
A)  $8 ( x - y ) ( x + 4 y )$ 
B)  $( 8 x - 8 y ) ( x + 4 y )$ 
C)  $( x - y ) ( 8 x + 24 y )$ 
D)  $8 ( x + y ) ( x - 4 y )$

Question 5

Factor.
-$$x ^ { 3 } + 6 x ^ { 2 } - 16 x$$

Accepted Answer

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

Question 6

Factor.
-$36 m ^ { 9 } - 18 m ^ { 4 } - 48 m ^ { 2 }$

Accepted Answer

A)  $m ^ { 2 } \left( 36 m ^ { 7 } - 18 m ^ { 2 } - 48 \right)$ 
B)  No common factor 
C)  $6 \left( 6 m ^ { 9 } - 3 m ^ { 4 } - 8 m ^ { 2 } \right)$ 
D)  $6 m ^ { 2 } \left( 6 m ^ { 7 } - 3 m ^ { 2 } - 8 \right)$ 
A)  $m ^ { 2 } \left( 36 m ^ { 7 } - 18 m ^ { 2 } - 48 \right)$ 
B)  No common factor 
C)  $6 \left( 6 m ^ { 9 } - 3 m ^ { 4 } - 8 m ^ { 2 } \right)$ 
D)  $6 m ^ { 2 } \left( 6 m ^ { 7 } - 3 m ^ { 2 } - 8 \right)$

Question 7

Factor.
-$$245 x ^ { 2 } + 350 x y + 125 y ^ { 2 }$$

Accepted Answer

A)  $5 \left( 49 x ^ { 2 } + 70 x y + 25 y \right)$ 
B)  $5 ( 7 x - 5 y ) ( 7 x + 5 y )$ 
C)  $( 35 x + 25 y ) ( 7 x + 5 y )$ 
D)  $5 ( 7 x + 5 y ) ^ { 2 }$ 
A)  $5 \left( 49 x ^ { 2 } + 70 x y + 25 y \right)$ 
B)  $5 ( 7 x - 5 y ) ( 7 x + 5 y )$ 
C)  $( 35 x + 25 y ) ( 7 x + 5 y )$ 
D)  $5 ( 7 x + 5 y ) ^ { 2 }$

Question 8

Factor.
-$$y ^ { 2 } + 1.6 y + 0.64$$

Accepted Answer

A)  $\left( y ^ { 2 } + 0.8 \right) ^ { 2 }$ 
B)  $( \mathrm { y } + 1.6 ) ^ { 2 }$ 
C)  $( y + 0.8 ) ^ { 2 }$ 
D)  $y ( y + 1$.6 
A)  $\left( y ^ { 2 } + 0.8 \right) ^ { 2 }$ 
B)  $( \mathrm { y } + 1.6 ) ^ { 2 }$ 
C)  $( y + 0.8 ) ^ { 2 }$ 
D)  $y ( y + 1$.6

Question 9

Factor.
-$5 \mathrm {~m} ( 2 - \mathrm { m } ) + 4 \mathrm { n } ( 2 - \mathrm { m } )$

Accepted Answer

A)  No common factor 
B)  $m ( 5 + 4 n ) ( 2 - 1 )$ 
C)  $( 5 m + 4 n ) ( 2 - m )$ 
D)  $( 5 m - 4 n ) ( 2 - m )$ 
A)  No common factor 
B)  $m ( 5 + 4 n ) ( 2 - 1 )$ 
C)  $( 5 m + 4 n ) ( 2 - m )$ 
D)  $( 5 m - 4 n ) ( 2 - m )$

Question 10

Factor.
-$$t ^ { 2 } + 0.8 t + 0.12$$

Accepted Answer

A)  Prime 
B)  $( t + 0.2 ) ( t + 0.6 )$ 
C)  $( t + 0.4 ) ^ { 2 }$ 
D)  $( t + 0.8 ) ( t + 0.12 )$ 
A)  Prime 
B)  $( t + 0.2 ) ( t + 0.6 )$ 
C)  $( t + 0.4 ) ^ { 2 }$ 
D)  $( t + 0.8 ) ( t + 0.12 )$

Question 11

Factor completely.
-$$x ^ { 2 } - 50 x + 625$$

Accepted Answer

A)  $( x + 25 ) ^ { 2 }$ 
B)  $( x - 25 ) ^ { 2 }$ 
C)  Prime 
D)  $( x + 25 ) ( x - 25 )$ 
A)  $( x + 25 ) ^ { 2 }$ 
B)  $( x - 25 ) ^ { 2 }$ 
C)  Prime 
D)  $( x + 25 ) ( x - 25 )$

Question 12

Factor by grouping.
-$12 x ^ { 4 } - 15 x ^ { 2 } - 8 x ^ { 2 } + 10$

Accepted Answer

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

Question 13

Factor completely.
-$$\mathrm { x } ^ { 2 } + 40 \mathrm { x } + 400$$

Accepted Answer

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

Question 14

Factor.
-$t ^ { 3 } + 27$

Accepted Answer

A)  $( t - 27 ) \left( t ^ { 2 } - 1 \right)$ 
B)  $( t + 3 ) \left( t ^ { 2 } - 3 t + 9 \right)$ 
C)  $( t - 3 ) \left( t ^ { 2 } + 3 t + 9 \right)$ 
D)  $( t + 3 ) \left( t ^ { 2 } + 9 \right)$ 
A)  $( t - 27 ) \left( t ^ { 2 } - 1 \right)$ 
B)  $( t + 3 ) \left( t ^ { 2 } - 3 t + 9 \right)$ 
C)  $( t - 3 ) \left( t ^ { 2 } + 3 t + 9 \right)$ 
D)  $( t + 3 ) \left( t ^ { 2 } + 9 \right)$

Question 15

Determine whether the following is a difference of squares.
-$$1 - y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 16

Factor.
-$15 x ^ { 2 } + 32 x + 16$

Accepted Answer

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

Question 17

Factor.
-$64 s ^ { 3 } + 1$

Accepted Answer

A)  $( 64 \mathrm {~s} + 1 ) \left( \mathrm { s } ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
B)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 1 \right)$ 
C)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
D)  $( 4 \mathrm {~s} - 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 4 \mathrm {~s} + 1 \right)$ 
A)  $( 64 \mathrm {~s} + 1 ) \left( \mathrm { s } ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
B)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 1 \right)$ 
C)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
D)  $( 4 \mathrm {~s} - 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 4 \mathrm {~s} + 1 \right)$

Question 18

Factor.
-$14 x ^ { 2 } - 49 x - 28$

Accepted Answer

A)  $7 ( 2 x - 1 ) ( x + 4 )$ 
B)  $( 2 x - 1 ) ( 7 x + 28 )$ 
C)  $( 14 x - 7 ) ( x + 4 )$ 
D)  $7 ( 2 x + 1 ) ( x - 4 )$ 
A)  $7 ( 2 x - 1 ) ( x + 4 )$ 
B)  $( 2 x - 1 ) ( 7 x + 28 )$ 
C)  $( 14 x - 7 ) ( x + 4 )$ 
D)  $7 ( 2 x + 1 ) ( x - 4 )$

Question 19

Factor.
-$$x ^ { 3 } - x ^ { 2 } - 72 x$$

Accepted Answer

A)  $\left( x ^ { 2 } + 1 \right) ( x - 72 )$ 
B)  $x ( x + 8 ) ( x - 9 )$ 
C)  Prime 
D)  $x ( x + 9 ) ( x - 8 )$ 
A)  $\left( x ^ { 2 } + 1 \right) ( x - 72 )$ 
B)  $x ( x + 8 ) ( x - 9 )$ 
C)  Prime 
D)  $x ( x + 9 ) ( x - 8 )$

Question 20

Factor by grouping.
-$20 x ^ { 2 } + 24 x y - 15 x y - 18 y ^ { 2 }$

Accepted Answer

A)  $( 4 x - 3 ) ( 5 x + 6 )$ 
B)  $( 4 x - 3 y ) ( 5 x + 6 y )$ 
C)  $( 4 x + 3 y ) ( 5 x + 6 y )$ 
D)  $( 20 x - 3 y ) ( x + 6 y )$ 
A)  $( 4 x - 3 ) ( 5 x + 6 )$ 
B)  $( 4 x - 3 y ) ( 5 x + 6 y )$ 
C)  $( 4 x + 3 y ) ( 5 x + 6 y )$ 
D)  $( 20 x - 3 y ) ( x + 6 y )$

Factor completely. - $49 x - 16 x ^ { 3 }$

Factor. - $3 x ^ { 2 } y ^ { 6 } + 6 x ^ { 2 } y ^ { 5 }$

Factor. - $u ^ { 2 } - 2 u v - 15 v ^ { 2 }$

Factor. - $8 x ^ { 2 } - 24 x y - 32 y ^ { 2 }$

Factor. - $x ^ { 3 } + 6 x ^ { 2 } - 16 x$

Factor. - $36 m ^ { 9 } - 18 m ^ { 4 } - 48 m ^ { 2 }$

Factor. - $245 x ^ { 2 } + 350 x y + 125 y ^ { 2 }$

Factor. - $y ^ { 2 } + 1.6 y + 0.64$

Factor. - $5 \mathrm {~m} ( 2 - \mathrm { m } ) + 4 \mathrm { n } ( 2 - \mathrm { m } )$

Factor. - $t ^ { 2 } + 0.8 t + 0.12$

Factor completely. - $x ^ { 2 } - 50 x + 625$

Factor by grouping. - $12 x ^ { 4 } - 15 x ^ { 2 } - 8 x ^ { 2 } + 10$

Factor completely. - $\mathrm { x } ^ { 2 } + 40 \mathrm { x } + 400$

Factor. - $t ^ { 3 } + 27$

Determine whether the following is a difference of squares. - $1 - y ^ { 2 }$

Factor. - $15 x ^ { 2 } + 32 x + 16$

Factor. - $64 s ^ { 3 } + 1$

Factor. - $14 x ^ { 2 } - 49 x - 28$

Factor. - $x ^ { 3 } - x ^ { 2 } - 72 x$

Factor by grouping. - $20 x ^ { 2 } + 24 x y - 15 x y - 18 y ^ { 2 }$

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

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 5: Polynomials: Factoring

Factor completely. - 49x−16x349 x - 16 x ^ { 3 }49x−16x3

Factor. - 3x2y6+6x2y53 x ^ { 2 } y ^ { 6 } + 6 x ^ { 2 } y ^ { 5 }3x2y6+6x2y5

Factor. - u2−2uv−15v2u ^ { 2 } - 2 u v - 15 v ^ { 2 }u2−2uv−15v2

Factor. - 8x2−24xy−32y28 x ^ { 2 } - 24 x y - 32 y ^ { 2 }8x2−24xy−32y2

Factor. - x3+6x2−16xx ^ { 3 } + 6 x ^ { 2 } - 16 xx3+6x2−16x

Factor. - 36m9−18m4−48m236 m ^ { 9 } - 18 m ^ { 4 } - 48 m ^ { 2 }36m9−18m4−48m2

Factor. - 245x2+350xy+125y2245 x ^ { 2 } + 350 x y + 125 y ^ { 2 }245x2+350xy+125y2

Factor. - y2+1.6y+0.64y ^ { 2 } + 1.6 y + 0.64y2+1.6y+0.64

Factor. - 5 m(2−m)+4n(2−m)5 \mathrm {~m} ( 2 - \mathrm { m } ) + 4 \mathrm { n } ( 2 - \mathrm { m } )5 m(2−m)+4n(2−m)

Factor. - t2+0.8t+0.12t ^ { 2 } + 0.8 t + 0.12t2+0.8t+0.12

Factor completely. - x2−50x+625x ^ { 2 } - 50 x + 625x2−50x+625

Factor by grouping. - 12x4−15x2−8x2+1012 x ^ { 4 } - 15 x ^ { 2 } - 8 x ^ { 2 } + 1012x4−15x2−8x2+10

Factor completely. - x2+40x+400\mathrm { x } ^ { 2 } + 40 \mathrm { x } + 400x2+40x+400

Factor. - t3+27t ^ { 3 } + 27t3+27

Determine whether the following is a difference of squares. - 1−y21 - y ^ { 2 }1−y2

Factor. - 15x2+32x+1615 x ^ { 2 } + 32 x + 1615x2+32x+16

Factor. - 64s3+164 s ^ { 3 } + 164s3+1

Factor. - 14x2−49x−2814 x ^ { 2 } - 49 x - 2814x2−49x−28

Factor. - x3−x2−72xx ^ { 3 } - x ^ { 2 } - 72 xx3−x2−72x

Factor by grouping. - 20x2+24xy−15xy−18y220 x ^ { 2 } + 24 x y - 15 x y - 18 y ^ { 2 }20x2+24xy−15xy−18y2