Question 1

Determine whether the following is a trinomial square.
-$$12 x ^ { 2 } - 52 x - 40$$

Accepted Answer

A) True 
 B)False

Question 2

Factor using the ac-method.
-$15 y ^ { 4 } + 2 y ^ { 2 } - 8$

Accepted Answer

A)  $\left( 15 y ^ { 2 } - 2 \right) \left( y ^ { 2 } + 4 \right)$ 
B)  $\left( 3 y ^ { 2 } - 2 \right) \left( 5 y ^ { 2 } + 4 \right)$ 
C)  $( 5 y - 4 ) ( 3 y + 2 )$ 
D)  $\left( 3 y ^ { 2 } + 1 \right) \left( 5 y ^ { 2 } - 8 \right)$ 
A)  $\left( 15 y ^ { 2 } - 2 \right) \left( y ^ { 2 } + 4 \right)$ 
B)  $\left( 3 y ^ { 2 } - 2 \right) \left( 5 y ^ { 2 } + 4 \right)$ 
C)  $( 5 y - 4 ) ( 3 y + 2 )$ 
D)  $\left( 3 y ^ { 2 } + 1 \right) \left( 5 y ^ { 2 } - 8 \right)$

Question 3

Factor using the ac-method.
-$$8 x ^ { 2 } - 10 x t - 3 t ^ { 2 }$$

Accepted Answer

A)  prime 
B)  $( 8 x + t ) ( x - 3 t )$ 
C)  $( 4 x - t ) ( 2 x + 3 t )$ 
D)  $( 4 x + t ) ( 2 x - 3 t )$ 
A)  prime 
B)  $( 8 x + t ) ( x - 3 t )$ 
C)  $( 4 x - t ) ( 2 x + 3 t )$ 
D)  $( 4 x + t ) ( 2 x - 3 t )$

Question 4

Factor.
-$729 p ^ { 3 } - 1$

Accepted Answer

A)  $( 729 p - 1 ) \left( p ^ { 2 } + 9 p + 1 \right)$ 
B)  $( 9 p - 1 ) \left( 81 p ^ { 2 } + 9 p + 1 \right)$ 
C)  $( 9 p - 1 ) \left( 81 p ^ { 2 } + 1 \right)$ 
D)  $( 9 p + 1 ) \left( 81 p ^ { 2 } - 9 p + 1 \right)$ 
A)  $( 729 p - 1 ) \left( p ^ { 2 } + 9 p + 1 \right)$ 
B)  $( 9 p - 1 ) \left( 81 p ^ { 2 } + 9 p + 1 \right)$ 
C)  $( 9 p - 1 ) \left( 81 p ^ { 2 } + 1 \right)$ 
D)  $( 9 p + 1 ) \left( 81 p ^ { 2 } - 9 p + 1 \right)$

Question 5

Factor completely.
-$$175 x ^ { 2 } - 28 y ^ { 2 }$$

Accepted Answer

A)  $7 ( 5 x + 2 y ) ( 5 x - 2 y )$ 
B)  $7 ( 5 x - 2 y ) ^ { 2 }$ 
C)  $( 5 x + 2 y ) ( 35 x - 14 y )$ 
D)  $( 35 x + 14 y ) ( 5 x - 2 y )$ 
A)  $7 ( 5 x + 2 y ) ( 5 x - 2 y )$ 
B)  $7 ( 5 x - 2 y ) ^ { 2 }$ 
C)  $( 5 x + 2 y ) ( 35 x - 14 y )$ 
D)  $( 35 x + 14 y ) ( 5 x - 2 y )$

Question 6

Factor.
-$$y ^ { 2 } + 0.6 y - 0.16$$

Accepted Answer

A)  $( y - 0.8 ) ( y - 0.2 )$ 
B)  $( \mathrm { y } + 0.8 ) ( \mathrm { y } - 0.2 )$ 
C)  $( y + 0.3 ) ^ { 2 }$ 
D)  $( \mathrm { y } - 0.8 ) ( \mathrm { y } + 0.2 )$ 
A)  $( y - 0.8 ) ( y - 0.2 )$ 
B)  $( \mathrm { y } + 0.8 ) ( \mathrm { y } - 0.2 )$ 
C)  $( y + 0.3 ) ^ { 2 }$ 
D)  $( \mathrm { y } - 0.8 ) ( \mathrm { y } + 0.2 )$

Question 7

Factor.
-$4 x ( 3 x - 2 ) - 3 ( 3 x - 2 )$

Accepted Answer

A)  $( 12 x - 3 ) ( x - 2 )$ 
B)  $( 4 x - 3 ) ( 3 x - 2 )$ 
C)  $( 4 x + 3 ) ( 3 x + 2 )$ 
D)  $( 12 x + 3 ) ( x + 2 )$ 
A)  $( 12 x - 3 ) ( x - 2 )$ 
B)  $( 4 x - 3 ) ( 3 x - 2 )$ 
C)  $( 4 x + 3 ) ( 3 x + 2 )$ 
D)  $( 12 x + 3 ) ( x + 2 )$

Question 8

Factor.
-$$5 \mathrm { x } ^ { 2 } + 15 \mathrm { x }$$

Accepted Answer

A)  $5 x ( x + 15 )$ 
B)  $5 x ( x + 3 )$ 
C)  $5 x ^ { 2 } ( x + 3 )$ 
D)  $x ( 5 x + 15 )$ 
A)  $5 x ( x + 15 )$ 
B)  $5 x ( x + 3 )$ 
C)  $5 x ^ { 2 } ( x + 3 )$ 
D)  $x ( 5 x + 15 )$

Question 9

Factor.
-$24 - 2 x - x ^ { 2 }$

Accepted Answer

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

Question 10

Factor by grouping.
-$$x ^ { 3 } + 5 x ^ { 2 } + 8 x + 40$$

Accepted Answer

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

Question 11

Factor completely.
-$16 x ^ { 2 } + 49$

Accepted Answer

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

Question 12

Factor.
-$12 z ^ { 2 } + 7 z y - 12 y ^ { 2 }$

Accepted Answer

A)  $( 12 z - 3 y ) ( z + 4 y )$ 
B)  $( 4 z + 3 y ) ( 3 z - 4 y )$ 
C)  $( 12 z + y ) ( z - 12 y )$ 
D)  $( 4 z - 3 y ) ( 3 z + 4 y )$ 
A)  $( 12 z - 3 y ) ( z + 4 y )$ 
B)  $( 4 z + 3 y ) ( 3 z - 4 y )$ 
C)  $( 12 z + y ) ( z - 12 y )$ 
D)  $( 4 z - 3 y ) ( 3 z + 4 y )$

Question 13

Determine whether the following is a difference of squares.
-$$t ^ { 3 } - 64$$

Accepted Answer

A) True 
 B)False

Question 14

Factor.
-$x ^ { 2 } - 6 x - 72$

Accepted Answer

A)  $( x - 6 ) ( x + 1 )$ 
B)  Prime 
C)  $( x - 6 ) ( x + 12 )$ 
D)  $( x + 6 ) ( x - 12 )$ 
A)  $( x - 6 ) ( x + 1 )$ 
B)  Prime 
C)  $( x - 6 ) ( x + 12 )$ 
D)  $( x + 6 ) ( x - 12 )$

Question 15

Factor completely.
-$$y ^ { 2 } - 36$$

Accepted Answer

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

Question 16

Factor completely.
-$$98 x ^ { 2 } - 128$$

Accepted Answer

A)  $2 ( 7 x + 8 ) ( 7 x - 8 )$ 
B)  $( 14 x + 16 ) ( 7 x - 8 )$ 
C)  $2 ( 7 x - 8 ) ^ { 2 }$ 
D)  $( 7 x + 8 ) ( 14 x - 16 )$ 
A)  $2 ( 7 x + 8 ) ( 7 x - 8 )$ 
B)  $( 14 x + 16 ) ( 7 x - 8 )$ 
C)  $2 ( 7 x - 8 ) ^ { 2 }$ 
D)  $( 7 x + 8 ) ( 14 x - 16 )$

Question 17

Factor completely.
-$x ^ { 4 } - 256$

Accepted Answer

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

Question 18

Factor completely.
-$$63 x ^ { 2 } - 7$$

Accepted Answer

A)  $( 3 x - 1 ) ( 21 x + 7 )$ 
B)  $7 ( 3 x - 1 ) ( 3 x + 1 )$ 
C)  $( 21 x - 7 ) ( 3 x + 1 )$ 
D)  $7 ( 3 x + 1 ) ^ { 2 }$ 
A)  $( 3 x - 1 ) ( 21 x + 7 )$ 
B)  $7 ( 3 x - 1 ) ( 3 x + 1 )$ 
C)  $( 21 x - 7 ) ( 3 x + 1 )$ 
D)  $7 ( 3 x + 1 ) ^ { 2 }$

Question 19

Factor completely.
-$49 y ^ { 4 } - 25$

Accepted Answer

A)  $\left( 7 y ^ { 2 } + 5 \right) ^ { 2 }$ 
B)  Prime 
C)  $\left( 7 y ^ { 2 } + 5 \right) \left( 7 y ^ { 2 } - 5 \right)$ 
D)  $\left( 7 y ^ { 2 } - 5 \right) ^ { 2 }$ 
A)  $\left( 7 y ^ { 2 } + 5 \right) ^ { 2 }$ 
B)  Prime 
C)  $\left( 7 y ^ { 2 } + 5 \right) \left( 7 y ^ { 2 } - 5 \right)$ 
D)  $\left( 7 y ^ { 2 } - 5 \right) ^ { 2 }$

Question 20

Factor.
-$$x ^ { 2 } + \frac { 6 } { 7 } x + \frac { 9 } { 49 }$$

Accepted Answer

A)  $\left( x + \frac { 6 } { 7 } \right) \left( x + \frac { 3 } { 7 } \right)$ 
B)  $\left( x ^ { 2 } + \frac { 3 } { 7 } \right) ^ { 2 }$ 
C)  $\left( x + \frac { 3 } { 7 } \right) ^ { 2 }$ 
D)  $\left( x + \frac { 3 } { 7 } \left( x + \frac { 3 } { 7 } x \right) \right.$ 
A)  $\left( x + \frac { 6 } { 7 } \right) \left( x + \frac { 3 } { 7 } \right)$ 
B)  $\left( x ^ { 2 } + \frac { 3 } { 7 } \right) ^ { 2 }$ 
C)  $\left( x + \frac { 3 } { 7 } \right) ^ { 2 }$ 
D)  $\left( x + \frac { 3 } { 7 } \left( x + \frac { 3 } { 7 } x \right) \right.$

Determine whether the following is a trinomial square. - $12 x ^ { 2 } - 52 x - 40$

Factor using the ac-method. - $15 y ^ { 4 } + 2 y ^ { 2 } - 8$

Factor using the ac-method. - $8 x ^ { 2 } - 10 x t - 3 t ^ { 2 }$

Factor. - $729 p ^ { 3 } - 1$

Factor completely. - $175 x ^ { 2 } - 28 y ^ { 2 }$

Factor. - $y ^ { 2 } + 0.6 y - 0.16$

Factor. - $4 x ( 3 x - 2 ) - 3 ( 3 x - 2 )$

Factor. - $5 \mathrm { x } ^ { 2 } + 15 \mathrm { x }$

Factor. - $24 - 2 x - x ^ { 2 }$

Factor by grouping. - $x ^ { 3 } + 5 x ^ { 2 } + 8 x + 40$

Factor completely. - $16 x ^ { 2 } + 49$

Factor. - $12 z ^ { 2 } + 7 z y - 12 y ^ { 2 }$

Determine whether the following is a difference of squares. - $t ^ { 3 } - 64$

Factor. - $x ^ { 2 } - 6 x - 72$

Factor completely. - $y ^ { 2 } - 36$

Factor completely. - $98 x ^ { 2 } - 128$

Factor completely. - $x ^ { 4 } - 256$

Factor completely. - $63 x ^ { 2 } - 7$

Factor completely. - $49 y ^ { 4 } - 25$

Factor. - $x ^ { 2 } + \frac { 6 } { 7 } x + \frac { 9 } { 49 }$

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

Determine whether the following is a trinomial square. - 12x2−52x−4012 x ^ { 2 } - 52 x - 4012x2−52x−40

Factor using the ac-method. - 15y4+2y2−815 y ^ { 4 } + 2 y ^ { 2 } - 815y4+2y2−8

Factor using the ac-method. - 8x2−10xt−3t28 x ^ { 2 } - 10 x t - 3 t ^ { 2 }8x2−10xt−3t2

Factor. - 729p3−1729 p ^ { 3 } - 1729p3−1

Factor completely. - 175x2−28y2175 x ^ { 2 } - 28 y ^ { 2 }175x2−28y2

Factor. - y2+0.6y−0.16y ^ { 2 } + 0.6 y - 0.16y2+0.6y−0.16

Factor. - 4x(3x−2)−3(3x−2)4 x ( 3 x - 2 ) - 3 ( 3 x - 2 )4x(3x−2)−3(3x−2)

Factor. - 5x2+15x5 \mathrm { x } ^ { 2 } + 15 \mathrm { x }5x2+15x

Factor. - 24−2x−x224 - 2 x - x ^ { 2 }24−2x−x2

Factor by grouping. - x3+5x2+8x+40x ^ { 3 } + 5 x ^ { 2 } + 8 x + 40x3+5x2+8x+40

Factor completely. - 16x2+4916 x ^ { 2 } + 4916x2+49

Factor. - 12z2+7zy−12y212 z ^ { 2 } + 7 z y - 12 y ^ { 2 }12z2+7zy−12y2

Determine whether the following is a difference of squares. - t3−64t ^ { 3 } - 64t3−64

Factor. - x2−6x−72x ^ { 2 } - 6 x - 72x2−6x−72

Factor completely. - y2−36y ^ { 2 } - 36y2−36

Factor completely. - 98x2−12898 x ^ { 2 } - 12898x2−128

Factor completely. - x4−256x ^ { 4 } - 256x4−256

Factor completely. - 63x2−763 x ^ { 2 } - 763x2−7

Factor completely. - 49y4−2549 y ^ { 4 } - 2549y4−25

Factor. - x2+67x+949x ^ { 2 } + \frac { 6 } { 7 } x + \frac { 9 } { 49 }x2+76​x+499​