Question 1

Factor the GCF out of the given expression.
-$$x ( 4 x + 5 ) - 5 ( 4 x + 5 )$$

Accepted Answer

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

Question 2

Factor by grouping.
-$$3 x ^ { 2 } + 8 x + 24 x + 64$$

Accepted Answer

A)  $( x - 8 ) ( 3 x - 8 )$ 
B)  $( 3 x + 8 ) ( 8 x + 3 )$ 
C)  $( 3 x + 8 ) ( 3 x + 8 )$ 
D)  $( x + 8 ) ( 3 x + 8 )$ 
A)  $( x - 8 ) ( 3 x - 8 )$ 
B)  $( 3 x + 8 ) ( 8 x + 3 )$ 
C)  $( 3 x + 8 ) ( 3 x + 8 )$ 
D)  $( x + 8 ) ( 3 x + 8 )$

Question 3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$27 a ^ { 3 } - 64 b ^ { 3 }$$

Accepted Answer

A)  $\left( 3 a + 4 b ^ { 2 } \right) \left( 9 a ^ { 2 } - 12 a b + 16 b ^ { 2 } \right)$ 
B)  $( 3 a - 4 b ) \left( 9 a ^ { 2 } + 16 b ^ { 2 } \right)$ 
C)  $( 3 a - 4 b ) \left( 9 a ^ { 2 } + 12 a b + 16 b ^ { 2 } \right)$ 
D)  $( 27 a - 4 b ) \left( a ^ { 2 } + 12 a b + 16 b ^ { 2 } \right)$ 
A)  $\left( 3 a + 4 b ^ { 2 } \right) \left( 9 a ^ { 2 } - 12 a b + 16 b ^ { 2 } \right)$ 
B)  $( 3 a - 4 b ) \left( 9 a ^ { 2 } + 16 b ^ { 2 } \right)$ 
C)  $( 3 a - 4 b ) \left( 9 a ^ { 2 } + 12 a b + 16 b ^ { 2 } \right)$ 
D)  $( 27 a - 4 b ) \left( a ^ { 2 } + 12 a b + 16 b ^ { 2 } \right)$

Question 4

Find the GCF.
-10,12,20

Accepted Answer

A)  4 
B)  1 
C)  10 
D)  2 
A)  4 
B)  1 
C)  10 
D)  2

Question 5

Find the GCF.
-57,95

Accepted Answer

A)  15 
B)  18 
C)  19 
D)  285 
A)  15 
B)  18 
C)  19 
D)  285

Question 6

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$49 y ^ { 4 } - 81$$

Accepted Answer

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

Question 7

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$x ^ { 3 } y ^ { 3 } - x ^ { 2 } y ^ { 5 }$

Accepted Answer

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

Question 8

Factor by grouping.
-$5 x ^ { 3 } - 15 x ^ { 2 } - 4 x + 12$

Accepted Answer

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

Question 9

Find the missing value such that the given binomial is a factor of the given polynomial.
-$x ^ { 2 } - 10 x + ? , x - 3$

Accepted Answer

A)  10 
B)  21 
C)  7 
D)  3 
A)  10 
B)  21 
C)  7 
D)  3

Question 10

Find the GCF.
-16s,24

Accepted Answer

A)  48s 
B)  16 
C)  8s 
D)  8 
A)  48s 
B)  16 
C)  8s 
D)  8

Question 11

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

Accepted Answer

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

Question 12

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$27 x ^ { 2 } + 18 x - 24$$

Accepted Answer

A)  $( 9 x - 6 ) ( 3 x + 4 )$ 
B)  $3 ( 3 x - 2 ) ( 3 x + 4 )$ 
C)  $( 3 x - 2 ) ( 9 x + 12 )$ 
D)  $3 ( 3 x + 2 ) ( 3 x - 4 )$ 
A)  $( 9 x - 6 ) ( 3 x + 4 )$ 
B)  $3 ( 3 x - 2 ) ( 3 x + 4 )$ 
C)  $( 3 x - 2 ) ( 9 x + 12 )$ 
D)  $3 ( 3 x + 2 ) ( 3 x - 4 )$

Question 13

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 15 feet by 17 feet and the area of the rug is 80 square feet, how wide will the border be?

Accepted Answer

A)  3.5 feet 
B)  6 feet 
C)  4.5 feet 
D)  5.5 feet 
A)  3.5 feet 
B)  6 feet 
C)  4.5 feet 
D)  5.5 feet

Question 14

Find the missing value such that the given binomial is a factor of the given polynomial.
-$$x ^ { 2 } + 15 x + ? , x + 3$$

Accepted Answer

A)  12 
B)  36 
C)  3 
D)  15 
A)  12 
B)  36 
C)  3 
D)  15

Question 15

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } - 4$$

Accepted Answer

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

Question 16

Factor by grouping.
-$20 x ^ { 2 } - 15 x - 16 x + 12$

Accepted Answer

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

Question 17

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$f ( x ) = 4 x ^ { 2 } + 3 x - 5 , f ( a - 1 )$$

Accepted Answer

A)  $4 a ^ { 2 } - 5 a + 2$ 
B)  $4 a ^ { 2 } - 17 a + 2$ 
C)  $4 a ^ { 2 } - 5 a - 4$ 
D)  $- 5 a ^ { 2 } + 4 a - 4$ 
A)  $4 a ^ { 2 } - 5 a + 2$ 
B)  $4 a ^ { 2 } - 17 a + 2$ 
C)  $4 a ^ { 2 } - 5 a - 4$ 
D)  $- 5 a ^ { 2 } + 4 a - 4$

Question 18

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } + 8 x + 15$$

Accepted Answer

A)  $( x + 15 ) ( x + 8 )$ 
B)  $( x - 5 ) ( x - 3 )$ 
C)  $( x + 15 ) ( x - 1 )$ 
D)  $( x + 5 ) ( x + 3 )$ 
A)  $( x + 15 ) ( x + 8 )$ 
B)  $( x - 5 ) ( x - 3 )$ 
C)  $( x + 15 ) ( x - 1 )$ 
D)  $( x + 5 ) ( x + 3 )$

Question 19

Find the missing value such that the given binomial is a factor of the given polynomial.
-$x ^ { 2 } - 3 x - ? , x + 4$

Accepted Answer

A)  4 
B)  3 
C)  28 
D)  7 
A)  4 
B)  3 
C)  28 
D)  7

Question 20

Determine which factoring technique is appropriate for the given polynomial.
-$$14 x ^ { 2 } - 32 x + 8$$

Accepted Answer

A)  trinomial, leading coefficient of 1 
B)  factoring by grouping 
C)  trinomial, leading coefficient other than 1 
D)  factor out GCF 
A)  trinomial, leading coefficient of 1 
B)  factoring by grouping 
C)  trinomial, leading coefficient other than 1 
D)  factor out GCF

Factor the GCF out of the given expression. - $x ( 4 x + 5 ) - 5 ( 4 x + 5 )$

Factor by grouping. - $3 x ^ { 2 } + 8 x + 24 x + 64$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $27 a ^ { 3 } - 64 b ^ { 3 }$

Find the GCF. -10,12,20

Find the GCF. -57,95

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $49 y ^ { 4 } - 81$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 3 } y ^ { 3 } - x ^ { 2 } y ^ { 5 }$

Factor by grouping. - $5 x ^ { 3 } - 15 x ^ { 2 } - 4 x + 12$

Find the missing value such that the given binomial is a factor of the given polynomial. - $x ^ { 2 } - 10 x + ? , x - 3$

Find the GCF. -16s,24

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

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $27 x ^ { 2 } + 18 x - 24$

Find the missing value such that the given binomial is a factor of the given polynomial. - $x ^ { 2 } + 15 x + ? , x + 3$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 4$

Factor by grouping. - $20 x ^ { 2 } - 15 x - 16 x + 12$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $f ( x ) = 4 x ^ { 2 } + 3 x - 5 , f ( a - 1 )$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } + 8 x + 15$

Find the missing value such that the given binomial is a factor of the given polynomial. - $x ^ { 2 } - 3 x - ? , x + 4$

Determine which factoring technique is appropriate for the given polynomial. - $14 x ^ { 2 } - 32 x + 8$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring and Quadratic Equations

Factor the GCF out of the given expression. - x(4x+5)−5(4x+5)x ( 4 x + 5 ) - 5 ( 4 x + 5 )x(4x+5)−5(4x+5)

Factor by grouping. - 3x2+8x+24x+643 x ^ { 2 } + 8 x + 24 x + 643x2+8x+24x+64

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 27a3−64b327 a ^ { 3 } - 64 b ^ { 3 }27a3−64b3