Question 1

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 5 x y - 14 y ^ { 2 }$

Accepted Answer

A)  $( x - 7 y ) ( x + y )$ 
B)  prime 
C)  $( x + 7 y ) ( x - 2 y )$ 
D)  $( x - 7 y ) ( x + 2 y )$ 
A)  $( x - 7 y ) ( x + y )$ 
B)  prime 
C)  $( x + 7 y ) ( x - 2 y )$ 
D)  $( x - 7 y ) ( x + 2 y )$

Question 2

Factor a negative number or a GCF with a negative coefficient from the polynomial.
-$- 2 x ^ { 5 } + x ^ { 8 }$

Accepted Answer

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

Question 3

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$16 x - x ^ { 5 }$

Accepted Answer

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

Question 4

Solve the equation.
-$x ( 5 x + 8 ) = 4$

Accepted Answer

A)  $0 , - \frac { 8 } { 5 }$ 
B)  $\frac { 2 } { 5 } , - 2$ 
C)  $\frac { 5 } { 2 } , 2$ 
D)  $0 , \frac { 8 } { 5 }$ 
A)  $0 , - \frac { 8 } { 5 }$ 
B)  $\frac { 2 } { 5 } , - 2$ 
C)  $\frac { 5 } { 2 } , 2$ 
D)  $0 , \frac { 8 } { 5 }$

Question 5

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$12 ( a + 13 ) - y ( a + 13 )$

Accepted Answer

A)  prime 
B)  $( a + 13 ) ( 12 - y )$ 
C)  $( a - 13 ) ( y - 12 )$ 
D)  $( a + 13 ) ( 12 + y )$ 
A)  prime 
B)  $( a + 13 ) ( 12 - y )$ 
C)  $( a - 13 ) ( y - 12 )$ 
D)  $( a + 13 ) ( 12 + y )$

Question 6

Solve the equation.
-$25 x ^ { 2 } - 1 = 0$

Accepted Answer

A)  $\frac { 1 } { 5 } , - \frac { 1 } { 5 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 } , 0$ 
A)  $\frac { 1 } { 5 } , - \frac { 1 } { 5 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 } , 0$

Question 7

Factor the four-term polynomial by grouping.
-$5 x y - 20 x + 9 y - 36$

Accepted Answer

A)  $( 5 x + y ) ( 9 y - 4 )$ 
B)  $( 5 x + 9 y ) ( y - 4 )$ 
C)  $( 5 x - 4 ) ( y + 9 )$ 
D)  $( 5 x + 9 ) ( y - 4 )$ 
A)  $( 5 x + y ) ( 9 y - 4 )$ 
B)  $( 5 x + 9 y ) ( y - 4 )$ 
C)  $( 5 x - 4 ) ( y + 9 )$ 
D)  $( 5 x + 9 ) ( y - 4 )$

Question 8

Factor the four-term polynomial by grouping.
-$2 x + 16 + x y + 8 y$

Accepted Answer

A)  $( x + 8 y ) ( 2 + y )$ 
B)  $( x + 8 ) ( 2 + y )$ 
C)  $( y + 8 ) ( x + 2 )$ 
D)  $( y + 8 ) ( 2 x + y )$ 
A)  $( x + 8 y ) ( 2 + y )$ 
B)  $( x + 8 ) ( 2 + y )$ 
C)  $( y + 8 ) ( x + 2 )$ 
D)  $( y + 8 ) ( 2 x + y )$

Question 9

Solve.
-The sum of two numbers is 13 and the sum of their squares is 97. Find the numbers.

Accepted Answer

A)  6 and 7 
B)  3 and 10 
C)  5 and 8 
D)  4 and 9 
A)  6 and 7 
B)  3 and 10 
C)  5 and 8 
D)  4 and 9

Question 10

Find the GCF for the list.
-40, 6, 15

Accepted Answer

A)  3 
B)  1 
C)  5 
D)  2 
A)  3 
B)  1 
C)  5 
D)  2

Question 11

Factor a negative number or a GCF with a negative coefficient from the polynomial.
-$- 18 y ^ { 3 } + 10 y$

Accepted Answer

A)  $- 2 y \left( 9 y ^ { 2 } + 5 \right)$ 
B)  $- 2 y ^ { 2 } ( 9 y - 5 )$ 
C)  $- 2 y \left( 9 y ^ { 2 } - 5 \right)$ 
D)  $- 2 \left( 9 y ^ { 3 } + 5 y \right)$ 
A)  $- 2 y \left( 9 y ^ { 2 } + 5 \right)$ 
B)  $- 2 y ^ { 2 } ( 9 y - 5 )$ 
C)  $- 2 y \left( 9 y ^ { 2 } - 5 \right)$ 
D)  $- 2 \left( 9 y ^ { 3 } + 5 y \right)$

Question 12

Factor completely.
-$8 z ^ { 2 } - 6 z - 9$

Accepted Answer

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

Question 13

Solve.
-The sum of a number and its square is 20 . Find the number.

Accepted Answer

A)  4 or 5 
B)  4 or $- 5$ 
C)  $- 4$ or 5 
D)  $- 4$ or $- 5$ 
A)  4 or 5 
B)  4 or $- 5$ 
C)  $- 4$ or 5 
D)  $- 4$ or $- 5$

Question 14

Factor out the GCF from the polynomial.
-$24 x ^ { 6 } y + 21 x y ^ { 4 }$

Accepted Answer

A)  $3 x y \left( 8 x ^ { 5 } + 7 y ^ { 3 } \right)$ 
B)  $3 x \left( 8 x ^ { 5 } y + 7 y ^ { 4 } \right)$ 
C)  $x y \left( 24 x ^ { 5 } + 21 y ^ { 3 } \right)$ 
D)  $3 y \left( 8 x ^ { 6 } + 7 x y ^ { 3 } \right)$ 
A)  $3 x y \left( 8 x ^ { 5 } + 7 y ^ { 3 } \right)$ 
B)  $3 x \left( 8 x ^ { 5 } y + 7 y ^ { 4 } \right)$ 
C)  $x y \left( 24 x ^ { 5 } + 21 y ^ { 3 } \right)$ 
D)  $3 y \left( 8 x ^ { 6 } + 7 x y ^ { 3 } \right)$

Question 15

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - 6 x - 27$

Accepted Answer

A)  $( x - 3 ) ( x + 1 )$ 
B)  prime 
C)  $( x - 3 ) ( x - 9 )$ 
D)  $( x + 3 ) ( x - 9 )$ 
A)  $( x - 3 ) ( x + 1 )$ 
B)  prime 
C)  $( x - 3 ) ( x - 9 )$ 
D)  $( x + 3 ) ( x - 9 )$

Question 16

Factor completely.
-$100 x ^ { 3 } + 120 x ^ { 2 } + 32 x$

Accepted Answer

A)  $x ( 20 x + 16 ) ( 5 x + 2 )$ 
B)  $x ( 5 x + 4 ) ( 20 x + 8 )$ 
C)  $4 x ( 5 x + 4 ) ( 5 x + 2 )$ 
D)  $4 \left( 5 x ^ { 2 } + 4 \right) ( 5 x + 2 )$ 
A)  $x ( 20 x + 16 ) ( 5 x + 2 )$ 
B)  $x ( 5 x + 4 ) ( 20 x + 8 )$ 
C)  $4 x ( 5 x + 4 ) ( 5 x + 2 )$ 
D)  $4 \left( 5 x ^ { 2 } + 4 \right) ( 5 x + 2 )$

Question 17

Factor completely.
-$6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 2 } - 20 y ^ { 2 }$

Accepted Answer

A)  $y ^ { 2 } ( x - 4 ) ( 6 x + 5 )$ 
B)  $( 3 x - 4 y ) ( 2 x + 5 y )$ 
C)  $( 2 x - 4 y ) ( 3 x + 5 y )$ 
D)  $y ^ { 2 } ( 3 x - 4 ) ( 2 x + 5 )$ 
A)  $y ^ { 2 } ( x - 4 ) ( 6 x + 5 )$ 
B)  $( 3 x - 4 y ) ( 2 x + 5 y )$ 
C)  $( 2 x - 4 y ) ( 3 x + 5 y )$ 
D)  $y ^ { 2 } ( 3 x - 4 ) ( 2 x + 5 )$

Question 18

Factor the binomial completely.
-$16 a ^ { 3 } - 9 a$

Accepted Answer

A)  $a ( 16 a + 1 ) ( a - 9 )$ 
B)  $a ( 4 a + 3 ) ( 4 a - 3 )$ 
C)  $a ( 4 a - 3 ) ^ { 2 }$ 
D)  $\left( 4 a ^ { 2 } + 3 \right) ( 4 a - 3 )$ 
A)  $a ( 16 a + 1 ) ( a - 9 )$ 
B)  $a ( 4 a + 3 ) ( 4 a - 3 )$ 
C)  $a ( 4 a - 3 ) ^ { 2 }$ 
D)  $\left( 4 a ^ { 2 } + 3 \right) ( 4 a - 3 )$

Question 19

Solve the equation.
-$16 x ^ { 3 } + 24 x ^ { 2 } + 5 x = 0$

Accepted Answer

A)  $\frac { 1 } { 4 } , \frac { 5 } { 4 } , 0$ 
B)  $- \frac { 5 } { 16 } , \frac { 5 } { 8 }$ 
C)  $- \frac { 1 } { 16 } , - \frac { 5 } { 16 }$ 
D)  $- \frac { 1 } { 4 } , - \frac { 5 } { 4 } , 0$ 
A)  $\frac { 1 } { 4 } , \frac { 5 } { 4 } , 0$ 
B)  $- \frac { 5 } { 16 } , \frac { 5 } { 8 }$ 
C)  $- \frac { 1 } { 16 } , - \frac { 5 } { 16 }$ 
D)  $- \frac { 1 } { 4 } , - \frac { 5 } { 4 } , 0$

Question 20

Factor out the GCF from the polynomial.
-$48 p + 12 q - 12$

Accepted Answer

A)  $12 p ( 4 + q - 1 )$ 
B)  $12 ( 4 p + q )$ 
C)  $12 ( 4 p + q - 1 )$ 
D)  no common factors 
A)  $12 p ( 4 + q - 1 )$ 
B)  $12 ( 4 p + q )$ 
C)  $12 ( 4 p + q - 1 )$ 
D)  no common factors

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 5 x y - 14 y ^ { 2 }$

Factor a negative number or a GCF with a negative coefficient from the polynomial. - $- 2 x ^ { 5 } + x ^ { 8 }$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $16 x - x ^ { 5 }$

Solve the equation. - $x ( 5 x + 8 ) = 4$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $12 ( a + 13 ) - y ( a + 13 )$

Solve the equation. - $25 x ^ { 2 } - 1 = 0$

Factor the four-term polynomial by grouping. - $5 x y - 20 x + 9 y - 36$

Factor the four-term polynomial by grouping. - $2 x + 16 + x y + 8 y$

Solve. -The sum of two numbers is 13 and the sum of their squares is 97. Find the numbers.

Find the GCF for the list. -40, 6, 15

Factor a negative number or a GCF with a negative coefficient from the polynomial. - $- 18 y ^ { 3 } + 10 y$

Factor completely. - $8 z ^ { 2 } - 6 z - 9$

Solve. -The sum of a number and its square is 20 . Find the number.

Factor out the GCF from the polynomial. - $24 x ^ { 6 } y + 21 x y ^ { 4 }$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - 6 x - 27$

Factor completely. - $100 x ^ { 3 } + 120 x ^ { 2 } + 32 x$

Factor completely. - $6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 2 } - 20 y ^ { 2 }$

Factor the binomial completely. - $16 a ^ { 3 } - 9 a$

Solve the equation. - $16 x ^ { 3 } + 24 x ^ { 2 } + 5 x = 0$

Factor out the GCF from the polynomial. - $48 p + 12 q - 12$

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

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - x2+5xy−14y2x ^ { 2 } + 5 x y - 14 y ^ { 2 }x2+5xy−14y2

Factor a negative number or a GCF with a negative coefficient from the polynomial. - −2x5+x8- 2 x ^ { 5 } + x ^ { 8 }−2x5+x8

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - 16x−x516 x - x ^ { 5 }16x−x5

Solve the equation. - x(5x+8)=4x ( 5 x + 8 ) = 4x(5x+8)=4

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - 12(a+13)−y(a+13)12 ( a + 13 ) - y ( a + 13 )12(a+13)−y(a+13)

Solve the equation. - 25x2−1=025 x ^ { 2 } - 1 = 025x2−1=0

Factor the four-term polynomial by grouping. - 5xy−20x+9y−365 x y - 20 x + 9 y - 365xy−20x+9y−36

Factor the four-term polynomial by grouping. - 2x+16+xy+8y2 x + 16 + x y + 8 y2x+16+xy+8y