Question 1

Solve the equation.
-$x ( x + 12 ) = 0$

Accepted Answer

A)  $- 1 , - 12$ 
B)  12,0 
C)  $- 12,0$ 
D)  $1 , - 12$ 
A)  $- 1 , - 12$ 
B)  12,0 
C)  $- 12,0$ 
D)  $1 , - 12$

Question 2

Find the x-intercepts of the graph of each equation.
-$y = 12 x ^ { 2 } + 23 x + 10$

Accepted Answer

A)  $\left( - \frac { 4 } { 5 } , 0 \right) , \left( - \frac { 2 } { 3 } , 0 \right)$ 
B)  $\left( \frac { 4 } { 5 } , 0 \right) , \left( \frac { 3 } { 2 } , 0 \right)$ 
C)  $\left( - \frac { 5 } { 4 } , 0 \right) , \left( - \frac { 2 } { 3 } , 0 \right)$ 
D)  $\left( \frac { 5 } { 4 } , 0 \right) , \left( \frac { 2 } { 3 } , 0 \right)$ 
A)  $\left( - \frac { 4 } { 5 } , 0 \right) , \left( - \frac { 2 } { 3 } , 0 \right)$ 
B)  $\left( \frac { 4 } { 5 } , 0 \right) , \left( \frac { 3 } { 2 } , 0 \right)$ 
C)  $\left( - \frac { 5 } { 4 } , 0 \right) , \left( - \frac { 2 } { 3 } , 0 \right)$ 
D)  $\left( \frac { 5 } { 4 } , 0 \right) , \left( \frac { 2 } { 3 } , 0 \right)$

Question 3

Find the GCF for the list.
-$14 m ^ { 4 } , 56 m ^ { 7 }$

Accepted Answer

A)  $14 \mathrm {~m} ^ { 3 }$ 
B)  $14 m ^ { 4 }$ 
C)  $784 \mathrm {~m} ^ { 3 }$ 
D)  $56 \mathrm {~m} ^ { 4 }$ 
A)  $14 \mathrm {~m} ^ { 3 }$ 
B)  $14 m ^ { 4 }$ 
C)  $784 \mathrm {~m} ^ { 3 }$ 
D)  $56 \mathrm {~m} ^ { 4 }$

Question 4

Solve the equation.
-$x ^ { 2 } - x = 56$

Accepted Answer

A)  1,56 
B)  7,8 
C)  $- 7 , - 8$ 
D)  $- 7,8$ 
A)  1,56 
B)  7,8 
C)  $- 7 , - 8$ 
D)  $- 7,8$

Question 5

Solve the equation.
-$4 t ^ { 3 } - 81 t = 0$

Accepted Answer

A)  0 
B)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 } , 0$ 
A)  0 
B)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 } , 0$

Question 6

Find the GCF for the list.
-9x, x

Accepted Answer

A)  9x 
B)  1 
C)  9 
D)  x 
A)  9x 
B)  1 
C)  9 
D)  x

Question 7

Solve the equation.
-$( 5 x - 3 ) \left( 25 x ^ { 2 } - 30 x + 9 \right) = 0$

Accepted Answer

A)  $\frac { 3 } { 5 } , 5,3,0$ 
B)  $\frac { 3 } { 5 }$ 
C)  $\frac { 3 } { 5 } , 0$ 
D)  $\frac { 3 } { 5 } , 5,3$ 
A)  $\frac { 3 } { 5 } , 5,3,0$ 
B)  $\frac { 3 } { 5 }$ 
C)  $\frac { 3 } { 5 } , 0$ 
D)  $\frac { 3 } { 5 } , 5,3$

Question 8

Factor the binomial completely.
-$50 x ^ { 2 } y - 98 y$

Accepted Answer

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

Question 9

Find the x-intercepts of the graph of each equation.
-$y = ( x - 6 ) ( x + 5 )$

Accepted Answer

A)  $( - 6,0 ) , ( - 5,0 )$ 
B)  $( 6,0 ) , ( 5,0 )$ 
C)  $( 6,0 ) , ( - 5,0 )$ 
D)  $( - 6,0 ) , ( 5,0 )$ 
A)  $( - 6,0 ) , ( - 5,0 )$ 
B)  $( 6,0 ) , ( 5,0 )$ 
C)  $( 6,0 ) , ( - 5,0 )$ 
D)  $( - 6,0 ) , ( 5,0 )$

Question 10

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 3 } y + 7 x ^ { 2 } y ^ { 2 } - 18 x y ^ { 3 }$

Accepted Answer

A)  $x y \left( x ^ { 2 } + 7 x - 18 y ^ { 2 } \right)$ 
B)  $x \left( x y - 2 y ^ { 2 } \right) ( x + 9 y )$ 
C)  $x y ( x - 2 y ) ( x + 9 y )$ 
D)  $y ( x - 2 y ) \left( x y + 9 y ^ { 2 } \right)$ 
A)  $x y \left( x ^ { 2 } + 7 x - 18 y ^ { 2 } \right)$ 
B)  $x \left( x y - 2 y ^ { 2 } \right) ( x + 9 y )$ 
C)  $x y ( x - 2 y ) ( x + 9 y )$ 
D)  $y ( x - 2 y ) \left( x y + 9 y ^ { 2 } \right)$

Question 11

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 7 x + 12$

Accepted Answer

A)  $( x + 4 ) ( x + 3 )$ 
B)  prime 
C)  $( x - 4 ) ( x + 3 )$ 
D)  $( x - 4 ) ( x + 1 )$ 
A)  $( x + 4 ) ( x + 3 )$ 
B)  prime 
C)  $( x - 4 ) ( x + 3 )$ 
D)  $( x - 4 ) ( x + 1 )$

Question 12

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$y ^ { 2 } + 40 y + 400$

Accepted Answer

A)  $( y - 20 ) ^ { 2 }$ 
B)  $( y + 20 ) ( y - 20 )$ 
C)  prime 
D)  $( \mathrm { y } + 20 ) ^ { 2 }$ 
A)  $( y - 20 ) ^ { 2 }$ 
B)  $( y + 20 ) ( y - 20 )$ 
C)  prime 
D)  $( \mathrm { y } + 20 ) ^ { 2 }$

Question 13

Factor out the GCF from the polynomial.
-$36 x ^ { 8 } y 8 + 36 x ^ { 4 } y ^ { 6 } + 60 x ^ { 2 } y ^ { 2 }$

Accepted Answer

A)  $12 x ^ { 2 } y ^ { 2 } \left( 3 x ^ { 6 } y ^ { 6 } + 3 x ^ { 2 } y ^ { 4 } + 5 \right)$ 
B)  $12 \left( 3 x ^ { 8 } y ^ { 8 } + 3 x ^ { 4 } y ^ { 6 } + 5 x ^ { 2 } y ^ { 2 } \right)$ 
C)  $12 x ^ { 2 } \left( 3 x ^ { 6 } y ^ { 8 } + 3 x ^ { 2 } y ^ { 6 } + 5 y ^ { 2 } \right)$ 
D)  no common factor 
A)  $12 x ^ { 2 } y ^ { 2 } \left( 3 x ^ { 6 } y ^ { 6 } + 3 x ^ { 2 } y ^ { 4 } + 5 \right)$ 
B)  $12 \left( 3 x ^ { 8 } y ^ { 8 } + 3 x ^ { 4 } y ^ { 6 } + 5 x ^ { 2 } y ^ { 2 } \right)$ 
C)  $12 x ^ { 2 } \left( 3 x ^ { 6 } y ^ { 8 } + 3 x ^ { 2 } y ^ { 6 } + 5 y ^ { 2 } \right)$ 
D)  no common factor

Question 14

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 2 x - 15$

Accepted Answer

A)  $( x + 5 ) ( x - 3 )$ 
B)  prime 
C)  $( x - 5 ) ( x + 1 )$ 
D)  $( x - 5 ) ( x + 3 )$ 
A)  $( x + 5 ) ( x - 3 )$ 
B)  prime 
C)  $( x - 5 ) ( x + 1 )$ 
D)  $( x - 5 ) ( x + 3 )$

Question 15

Find the GCF for the list.
-28x, 4

Accepted Answer

A)  1 
B)  4 
C)  7x 
D)  28x 
A)  1 
B)  4 
C)  7x 
D)  28x

Question 16

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 4 } - 4 x ^ { 2 } - 77$

Accepted Answer

A)  prime 
B)  $\left( x ^ { 2 } - 11 \right) \left( x ^ { 2 } + 7 \right)$ 
C)  $\left( x ^ { 2 } - 77 \right) \left( x ^ { 2 } + 1 \right)$ 
D)  $\left( x ^ { 2 } + 11 \right) \left( x ^ { 2 } - 7 \right)$ 
A)  prime 
B)  $\left( x ^ { 2 } - 11 \right) \left( x ^ { 2 } + 7 \right)$ 
C)  $\left( x ^ { 2 } - 77 \right) \left( x ^ { 2 } + 1 \right)$ 
D)  $\left( x ^ { 2 } + 11 \right) \left( x ^ { 2 } - 7 \right)$

Question 17

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - x - 30$

Accepted Answer

A)  $( x + 6 ) ( x - 5 )$ 
B)  prime 
C)  $( x + 1 ) ( x - 30 )$ 
D)  $( x + 5 ) ( x - 6 )$ 
A)  $( x + 6 ) ( x - 5 )$ 
B)  prime 
C)  $( x + 1 ) ( x - 30 )$ 
D)  $( x + 5 ) ( x - 6 )$

Question 18

Solve.
-The width of a rectangle is 6 kilometers less than twice its length. If its area is 140 square kilometers, find the dimensions of the rectangle.

Accepted Answer

A)  length $= 10 \mathrm {~km}$, width $= 14 \mathrm {~km}$ 
B)  length $= 3 \mathrm {~km}$, width $= \frac { 140 } { 3 } \mathrm {~km}$ 
C)  width $= 10 \mathrm {~km}$, length $= 14 \mathrm {~km}$ 
D)  length $= 7 \mathrm {~km}$, width $= 8 \mathrm {~km}$ 
A)  length $= 10 \mathrm {~km}$, width $= 14 \mathrm {~km}$ 
B)  length $= 3 \mathrm {~km}$, width $= \frac { 140 } { 3 } \mathrm {~km}$ 
C)  width $= 10 \mathrm {~km}$, length $= 14 \mathrm {~km}$ 
D)  length $= 7 \mathrm {~km}$, width $= 8 \mathrm {~km}$

Question 19

Solve.
-The perimeter of the quadrilateral is 40 inches. Find the lengths of the sides.

Accepted Answer

A)  8 in., 13 in., 18 in., 1 in. 
B)  7 in., 14 in., 18 in., 1 in. 
C)  9 in., 15 in., 28 in., 2 in. 
D)  3 in., 3 in., $- 2$ in., $- 4$ in. 
A)  8 in., 13 in., 18 in., 1 in. 
B)  7 in., 14 in., 18 in., 1 in. 
C)  9 in., 15 in., 28 in., 2 in. 
D)  3 in., 3 in., $- 2$ in., $- 4$ in.

Question 20

Factor completely.
-$12 x ^ { 2 } - 17 x y + 6 y ^ { 2 }$

Accepted Answer

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

Solve the equation. - $x ( x + 12 ) = 0$

Find the x-intercepts of the graph of each equation. - $y = 12 x ^ { 2 } + 23 x + 10$

Find the GCF for the list. - $14 m ^ { 4 } , 56 m ^ { 7 }$

Solve the equation. - $x ^ { 2 } - x = 56$

Solve the equation. - $4 t ^ { 3 } - 81 t = 0$

Find the GCF for the list. -9x, x

Solve the equation. - $( 5 x - 3 ) \left( 25 x ^ { 2 } - 30 x + 9 \right) = 0$

Factor the binomial completely. - $50 x ^ { 2 } y - 98 y$

Find the x-intercepts of the graph of each equation. - $y = ( x - 6 ) ( x + 5 )$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 3 } y + 7 x ^ { 2 } y ^ { 2 } - 18 x y ^ { 3 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 7 x + 12$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $y ^ { 2 } + 40 y + 400$

Factor out the GCF from the polynomial. - $36 x ^ { 8 } y 8 + 36 x ^ { 4 } y ^ { 6 } + 60 x ^ { 2 } y ^ { 2 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 2 x - 15$

Find the GCF for the list. -28x, 4

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 4 } - 4 x ^ { 2 } - 77$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - x - 30$

Solve. -The width of a rectangle is 6 kilometers less than twice its length. If its area is 140 square kilometers, find the dimensions of the rectangle.

Solve. -The perimeter of the quadrilateral is 40 inches. Find the lengths of the sides.

Factor completely. - $12 x ^ { 2 } - 17 x y + 6 y ^ { 2 }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring Polynomials

Solve the equation. - x(x+12)=0x ( x + 12 ) = 0x(x+12)=0

Find the x-intercepts of the graph of each equation. - y=12x2+23x+10y = 12 x ^ { 2 } + 23 x + 10y=12x2+23x+10

Find the GCF for the list. - 14m4,56m714 m ^ { 4 } , 56 m ^ { 7 }14m4,56m7

Solve the equation. - x2−x=56x ^ { 2 } - x = 56x2−x=56

Solve the equation. - 4t3−81t=04 t ^ { 3 } - 81 t = 04t3−81t=0