Question 1

Factor.
-$$12 x ^ { 2 } + 13 x t + 3 t ^ { 2 }$$

Accepted Answer

A)  $( 3 x - t ) ( 4 x - 3 t )$ 
B)  $( 12 x + t ) ( x + 3 t )$ 
C)  Prime 
D)  $( 3 x + t ) ( 4 x + 3 t )$ 
A)  $( 3 x - t ) ( 4 x - 3 t )$ 
B)  $( 12 x + t ) ( x + 3 t )$ 
C)  Prime 
D)  $( 3 x + t ) ( 4 x + 3 t )$

Question 2

Factor.
-$$x ^ { 6 } - 17 x y ^ { 5 } + 37 x ^ { 3 } y ^ { 6 } - 47 x ^ { 6 } y ^ { 5 }$$

Accepted Answer

A)  $x \left( x ^ { 5 } - 17 y ^ { 5 } + 37 x ^ { 2 } y ^ { 6 } - 47 x ^ { 5 } y ^ { 5 } \right)$ 
B)  $x y ^ { 5 } \left( x ^ { 5 } - 17 + 37 x ^ { 2 } y ^ { 1 } - 47 x ^ { 5 } \right)$ 
C)  $x ^ { 2 } \left( x ^ { 5 } - 17 y ^ { 4 } + 37 x ^ { 2 } y ^ { 5 } - 47 x ^ { 5 } y ^ { 4 } \right)$ 
D)  $x y \left( x ^ { 5 } - 17 y ^ { 4 } + 37 x ^ { 2 } y ^ { 5 } - 47 x ^ { 5 } y ^ { 4 } \right)$ 
A)  $x \left( x ^ { 5 } - 17 y ^ { 5 } + 37 x ^ { 2 } y ^ { 6 } - 47 x ^ { 5 } y ^ { 5 } \right)$ 
B)  $x y ^ { 5 } \left( x ^ { 5 } - 17 + 37 x ^ { 2 } y ^ { 1 } - 47 x ^ { 5 } \right)$ 
C)  $x ^ { 2 } \left( x ^ { 5 } - 17 y ^ { 4 } + 37 x ^ { 2 } y ^ { 5 } - 47 x ^ { 5 } y ^ { 4 } \right)$ 
D)  $x y \left( x ^ { 5 } - 17 y ^ { 4 } + 37 x ^ { 2 } y ^ { 5 } - 47 x ^ { 5 } y ^ { 4 } \right)$

Question 3

Factor.
-$$9 x ^ { 4 } - 18 x ^ { 3 } + 8 x ^ { 2 }$$

Accepted Answer

A)  $\left( 9 x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 4 \right)$ 
B)  $x ( 3 x + 2 ) ( 3 x + 4 )$ 
C)  $x ^ { 2 } ( 9 x - 1 ) ( x - 8 )$ 
D)  $x ^ { 2 } ( 3 x - 2 ) ( 3 x - 4 )$ 
A)  $\left( 9 x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 4 \right)$ 
B)  $x ( 3 x + 2 ) ( 3 x + 4 )$ 
C)  $x ^ { 2 } ( 9 x - 1 ) ( x - 8 )$ 
D)  $x ^ { 2 } ( 3 x - 2 ) ( 3 x - 4 )$

Question 4

Factor completely.
-$$25 + 10 x + x ^ { 2 }$$

Accepted Answer

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

Question 5

Factor completely.
-$64 m ^ { 2 } - \frac { 4 } { 9 }$

Accepted Answer

A)  $\left( 8 m + \frac { 2 } { 3 } \right) ^ { 2 }$ 
B)  prime 
C)  $\left( 8 m - \frac { 2 } { 3 } \right) ^ { 2 }$ 
D)  $\left( 8 m + \frac { 2 } { 3 } \right) \left( 8 m - \frac { 2 } { 3 } \right)$ 
A)  $\left( 8 m + \frac { 2 } { 3 } \right) ^ { 2 }$ 
B)  prime 
C)  $\left( 8 m - \frac { 2 } { 3 } \right) ^ { 2 }$ 
D)  $\left( 8 m + \frac { 2 } { 3 } \right) \left( 8 m - \frac { 2 } { 3 } \right)$

Question 6

Determine whether the following is a trinomial square.
-$$x ^ { 2 } - 14 x y + 49 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 7

Factor using the ac-method.
-$$6 x ^ { 4 } + 13 x ^ { 2 } + 6$$

Accepted Answer

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

Question 8

Factor.
-$$3 a ^ { 3 } + 6 a ^ { 2 } - 45 a$$

Accepted Answer

A)  $3 a ( a + 5 ) ( a + 3 )$ 
B)  $3 a ( a - 5 ) ( a + 3 )$ 
C)  $3 a ( a + 5 ) ( a - 3 )$ 
D)  $3 a ( a - 5 ) ( a - 3 )$ 
A)  $3 a ( a + 5 ) ( a + 3 )$ 
B)  $3 a ( a - 5 ) ( a + 3 )$ 
C)  $3 a ( a + 5 ) ( a - 3 )$ 
D)  $3 a ( a - 5 ) ( a - 3 )$

Question 9

Factor.
-$u ^ { 2 } - 2 u v - 24 v ^ { 2 }$

Accepted Answer

A)  $( u - v ) ( u + 6 v )$ 
B)  $( u - 4 v ) ( u + 6 v )$ 
C)  $( u - 4 v ) ( u + v )$ 
D)  $( u + 4 v ) ( u - 6 v )$ 
A)  $( u - v ) ( u + 6 v )$ 
B)  $( u - 4 v ) ( u + 6 v )$ 
C)  $( u - 4 v ) ( u + v )$ 
D)  $( u + 4 v ) ( u - 6 v )$

Question 10

Determine whether the following is a difference of squares.
-$$- 64 x ^ { 2 } + 64 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 11

Factor.
-$$\mathrm { t } ^ { 2 } + 0.2 \mathrm { t } - 0.24$$

Accepted Answer

A)  $( t + 0.24 ) ( t - 1 )$ 
B)  $( t + 0.6 ) ( t - 0.4 )$ 
C)  $( t - 0.6 ) ( t + 0.4 )$ 
D)  $( t + 0.1 ) ^ { 2 }$ 
A)  $( t + 0.24 ) ( t - 1 )$ 
B)  $( t + 0.6 ) ( t - 0.4 )$ 
C)  $( t - 0.6 ) ( t + 0.4 )$ 
D)  $( t + 0.1 ) ^ { 2 }$

Question 12

Factor completely.
-$$x ^ { 2 } + 2 x y - 24 y ^ { 2 }$$

Accepted Answer

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

Question 13

Factor.
-$$\frac { 5 } { 3 } x ^ { 7 } - \frac { 4 } { 3 } x ^ { 6 } + \frac { 8 } { 3 } x ^ { 5 } + \frac { 1 } { 3 } x ^ { 4 }$$

Accepted Answer

A)  $\frac { 1 } { 3 } x ^ { 5 } \left( 5 x ^ { 4 } - 4 x ^ { 3 } + 8 x ^ { 2 } + x \right)$ 
B)  $\frac { 1 } { 3 } x ^ { 5 } \left( 5 x ^ { 3 } + 4 x ^ { 2 } - 8 x - 1 \right)$ 
C)  $\frac { 5 } { 3 } x ^ { 4 } \left( x ^ { 3 } - 3 x ^ { 2 } + 7 x + 1 \right)$ 
D)  $\frac { 1 } { 3 } x ^ { 4 } \left( 5 x ^ { 3 } - 4 x ^ { 2 } + 8 x + 1 \right)$ 
A)  $\frac { 1 } { 3 } x ^ { 5 } \left( 5 x ^ { 4 } - 4 x ^ { 3 } + 8 x ^ { 2 } + x \right)$ 
B)  $\frac { 1 } { 3 } x ^ { 5 } \left( 5 x ^ { 3 } + 4 x ^ { 2 } - 8 x - 1 \right)$ 
C)  $\frac { 5 } { 3 } x ^ { 4 } \left( x ^ { 3 } - 3 x ^ { 2 } + 7 x + 1 \right)$ 
D)  $\frac { 1 } { 3 } x ^ { 4 } \left( 5 x ^ { 3 } - 4 x ^ { 2 } + 8 x + 1 \right)$

Question 14

Determine whether the following is a difference of squares.
-$$49 x ^ { 2 } - 19 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 15

Factor completely.
-$2 x ^ { 4 } - 2$

Accepted Answer

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

Question 16

Determine whether the following is a trinomial square.
-$$x ^ { 2 } - 8 x - 16$$

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

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

Question 18

Factor.
-$$9 m ^ { 8 } - 21 m ^ { 6 } - 27 m ^ { 4 }$$

Accepted Answer

A)  $3 m ^ { 4 } \left( 3 m ^ { 4 } - 7 m ^ { 2 } - 9 \right)$ 
B)  No common factor 
C)  $m ^ { 4 } \left( 9 m ^ { 4 } - 21 m ^ { 2 } - 27 \right)$ 
D)  $3 \left( 3 m ^ { 8 } - 7 m ^ { 6 } - 9 m ^ { 4 } \right)$ 
A)  $3 m ^ { 4 } \left( 3 m ^ { 4 } - 7 m ^ { 2 } - 9 \right)$ 
B)  No common factor 
C)  $m ^ { 4 } \left( 9 m ^ { 4 } - 21 m ^ { 2 } - 27 \right)$ 
D)  $3 \left( 3 m ^ { 8 } - 7 m ^ { 6 } - 9 m ^ { 4 } \right)$

Question 19

Factor completely.
-$$64 x ^ { 2 } - 9$$

Accepted Answer

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

Question 20

Determine whether the following is a difference of squares.
-$$49 x ^ { 2 } - 9 y ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Factor. - $12 x ^ { 2 } + 13 x t + 3 t ^ { 2 }$

Factor. - $x ^ { 6 } - 17 x y ^ { 5 } + 37 x ^ { 3 } y ^ { 6 } - 47 x ^ { 6 } y ^ { 5 }$

Factor. - $9 x ^ { 4 } - 18 x ^ { 3 } + 8 x ^ { 2 }$

Factor completely. - $25 + 10 x + x ^ { 2 }$

Factor completely. - $64 m ^ { 2 } - \frac { 4 } { 9 }$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 14 x y + 49 y ^ { 2 }$

Factor using the ac-method. - $6 x ^ { 4 } + 13 x ^ { 2 } + 6$

Factor. - $3 a ^ { 3 } + 6 a ^ { 2 } - 45 a$

Factor. - $u ^ { 2 } - 2 u v - 24 v ^ { 2 }$

Determine whether the following is a difference of squares. - $- 64 x ^ { 2 } + 64 y ^ { 2 }$

Factor. - $\mathrm { t } ^ { 2 } + 0.2 \mathrm { t } - 0.24$

Factor completely. - $x ^ { 2 } + 2 x y - 24 y ^ { 2 }$

Factor. - $\frac { 5 } { 3 } x ^ { 7 } - \frac { 4 } { 3 } x ^ { 6 } + \frac { 8 } { 3 } x ^ { 5 } + \frac { 1 } { 3 } x ^ { 4 }$

Determine whether the following is a difference of squares. - $49 x ^ { 2 } - 19 y ^ { 2 }$

Factor completely. - $2 x ^ { 4 } - 2$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 8 x - 16$

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

Factor. - $9 m ^ { 8 } - 21 m ^ { 6 } - 27 m ^ { 4 }$

Factor completely. - $64 x ^ { 2 } - 9$

Determine whether the following is a difference of squares. - $49 x ^ { 2 } - 9 y ^ { 2 }$

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. - 12x2+13xt+3t212 x ^ { 2 } + 13 x t + 3 t ^ { 2 }12x2+13xt+3t2

Factor. - x6−17xy5+37x3y6−47x6y5x ^ { 6 } - 17 x y ^ { 5 } + 37 x ^ { 3 } y ^ { 6 } - 47 x ^ { 6 } y ^ { 5 }x6−17xy5+37x3y6−47x6y5

Factor. - 9x4−18x3+8x29 x ^ { 4 } - 18 x ^ { 3 } + 8 x ^ { 2 }9x4−18x3+8x2

Factor completely. - 25+10x+x225 + 10 x + x ^ { 2 }25+10x+x2

Factor completely. - 64m2−4964 m ^ { 2 } - \frac { 4 } { 9 }64m2−94​

Determine whether the following is a trinomial square. - x2−14xy+49y2x ^ { 2 } - 14 x y + 49 y ^ { 2 }x2−14xy+49y2

Factor using the ac-method. - 6x4+13x2+66 x ^ { 4 } + 13 x ^ { 2 } + 66x4+13x2+6

Factor. - 3a3+6a2−45a3 a ^ { 3 } + 6 a ^ { 2 } - 45 a3a3+6a2−45a

Factor. - u2−2uv−24v2u ^ { 2 } - 2 u v - 24 v ^ { 2 }u2−2uv−24v2

Determine whether the following is a difference of squares. - −64x2+64y2- 64 x ^ { 2 } + 64 y ^ { 2 }−64x2+64y2

Factor. - t2+0.2t−0.24\mathrm { t } ^ { 2 } + 0.2 \mathrm { t } - 0.24t2+0.2t−0.24

Factor completely. - x2+2xy−24y2x ^ { 2 } + 2 x y - 24 y ^ { 2 }x2+2xy−24y2

Factor. - 53x7−43x6+83x5+13x4\frac { 5 } { 3 } x ^ { 7 } - \frac { 4 } { 3 } x ^ { 6 } + \frac { 8 } { 3 } x ^ { 5 } + \frac { 1 } { 3 } x ^ { 4 }35​x7−34​x6+38​x5+31​x4

Determine whether the following is a difference of squares. - 49x2−19y249 x ^ { 2 } - 19 y ^ { 2 }49x2−19y2

Factor completely. - 2x4−22 x ^ { 4 } - 22x4−2

Determine whether the following is a trinomial square. - x2−8x−16x ^ { 2 } - 8 x - 16x2−8x−16

Factor. - p6+1p ^ { 6 } + 1p6+1

Factor. - 9m8−21m6−27m49 m ^ { 8 } - 21 m ^ { 6 } - 27 m ^ { 4 }9m8−21m6−27m4

Factor completely. - 64x2−964 x ^ { 2 } - 964x2−9

Determine whether the following is a difference of squares. - 49x2−9y249 x ^ { 2 } - 9 y ^ { 2 }49x2−9y2

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

Factor. - $12 x ^ { 2 } + 13 x t + 3 t ^ { 2 }$

Factor. - $x ^ { 6 } - 17 x y ^ { 5 } + 37 x ^ { 3 } y ^ { 6 } - 47 x ^ { 6 } y ^ { 5 }$

Factor. - $9 x ^ { 4 } - 18 x ^ { 3 } + 8 x ^ { 2 }$

Factor completely. - $25 + 10 x + x ^ { 2 }$

Factor completely. - $64 m ^ { 2 } - \frac { 4 } { 9 }$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 14 x y + 49 y ^ { 2 }$

Factor using the ac-method. - $6 x ^ { 4 } + 13 x ^ { 2 } + 6$

Factor. - $3 a ^ { 3 } + 6 a ^ { 2 } - 45 a$

Factor. - $u ^ { 2 } - 2 u v - 24 v ^ { 2 }$

Determine whether the following is a difference of squares. - $- 64 x ^ { 2 } + 64 y ^ { 2 }$

Factor. - $\mathrm { t } ^ { 2 } + 0.2 \mathrm { t } - 0.24$

Factor completely. - $x ^ { 2 } + 2 x y - 24 y ^ { 2 }$

Factor. - $\frac { 5 } { 3 } x ^ { 7 } - \frac { 4 } { 3 } x ^ { 6 } + \frac { 8 } { 3 } x ^ { 5 } + \frac { 1 } { 3 } x ^ { 4 }$

Determine whether the following is a difference of squares. - $49 x ^ { 2 } - 19 y ^ { 2 }$

Factor completely. - $2 x ^ { 4 } - 2$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 8 x - 16$

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

Factor. - $9 m ^ { 8 } - 21 m ^ { 6 } - 27 m ^ { 4 }$

Factor completely. - $64 x ^ { 2 } - 9$

Determine whether the following is a difference of squares. - $49 x ^ { 2 } - 9 y ^ { 2 }$