Question 1

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$5 x ^ { 2 } - 33 x - 56$

Accepted Answer

A)  $( x - 7 ) ( x - 8 )$ 
B)  $( 5 x + 7 ) ( x - 8 )$ 
C)  $( 7 x + 5 ) ( x - 8 )$ 
D)  $( x + 5 ) ( x - 8 )$ 
A)  $( x - 7 ) ( x - 8 )$ 
B)  $( 5 x + 7 ) ( x - 8 )$ 
C)  $( 7 x + 5 ) ( x - 8 )$ 
D)  $( x + 5 ) ( x - 8 )$

Question 2

Factor the GCF out of the given expression.
-$17 x ^ { 8 } + 17 x$

Accepted Answer

A)  $17 x \left( x ^ { 7 } \right)$ 
B)  $17 \left( x ^ { 8 } + x \right)$ 
C)  $17 x \left( x ^ { 7 } + 1 \right)$ 
D)  $17 \left( x ^ { 9 } + 1 \right)$ 
A)  $17 x \left( x ^ { 7 } \right)$ 
B)  $17 \left( x ^ { 8 } + x \right)$ 
C)  $17 x \left( x ^ { 7 } + 1 \right)$ 
D)  $17 \left( x ^ { 9 } + 1 \right)$

Question 3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$x ^ { 2 } - 7 x y + 12 y ^ { 2 }$

Accepted Answer

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

Question 4

Choose the polynomial that has the given factor.
-x + 7

Accepted Answer

A)  $x ^ { 2 } - 12 x + 35$ 
B)  $x ^ { 3 } + 7 x ^ { 2 } - 175$ 
C)  $x ^ { 2 } + 7 x + 49$ 
D)  $x ^ { 3 } + 7 x ^ { 2 } - 25 x - 175$ 
A)  $x ^ { 2 } - 12 x + 35$ 
B)  $x ^ { 3 } + 7 x ^ { 2 } - 175$ 
C)  $x ^ { 2 } + 7 x + 49$ 
D)  $x ^ { 3 } + 7 x ^ { 2 } - 25 x - 175$

Question 5

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$5 x ^ { 5 } + 10 x ^ { 4 } y - 75 x ^ { 3 } y ^ { 2 }$$

Accepted Answer

A)  $5 x ^ { 3 } ( x - 3 y ) ( x + 5 y )$ 
B)  $\left( 5 x ^ { 2 } + 15 x y \right) \left( x ^ { 3 } - 5 y \right)$ 
C)  $( x - 3 y ) \left( 5 x ^ { 4 } + 25 x y \right)$ 
D)  $5 x ^ { 3 } ( x + 3 y ) ( x - 5 y )$ 
A)  $5 x ^ { 3 } ( x - 3 y ) ( x + 5 y )$ 
B)  $\left( 5 x ^ { 2 } + 15 x y \right) \left( x ^ { 3 } - 5 y \right)$ 
C)  $( x - 3 y ) \left( 5 x ^ { 4 } + 25 x y \right)$ 
D)  $5 x ^ { 3 } ( x + 3 y ) ( x - 5 y )$

Question 6

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$24 x ^ { 6 } + 66 x ^ { 4 } + 45 x ^ { 2 }$$

Accepted Answer

A)  $3 x ^ { 2 } \left( 2 x ^ { 2 } - 3 \right) \left( 4 x ^ { 2 } - 5 \right)$ 
B)  $3 x ^ { 2 } \left( 4 x ^ { 2 } + 5 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
C)  $3 \left( 4 x ^ { 4 } + 5 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
D)  $\left( 12 x ^ { 3 } + 15 \right) \left( 2 x ^ { 3 } + 3 \right)$ 
A)  $3 x ^ { 2 } \left( 2 x ^ { 2 } - 3 \right) \left( 4 x ^ { 2 } - 5 \right)$ 
B)  $3 x ^ { 2 } \left( 4 x ^ { 2 } + 5 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
C)  $3 \left( 4 x ^ { 4 } + 5 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
D)  $\left( 12 x ^ { 3 } + 15 \right) \left( 2 x ^ { 3 } + 3 \right)$

Question 7

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$x ^ { 2 } - 4 x - 45$

Accepted Answer

A)  $( x - 5 ) ( x + 9 )$ 
B)  $( x - 5 ) ( x + 1 )$ 
C)  $( x + 5 ) ( x - 9 )$ 
D)  Prime 
A)  $( x - 5 ) ( x + 9 )$ 
B)  $( x - 5 ) ( x + 1 )$ 
C)  $( x + 5 ) ( x - 9 )$ 
D)  Prime

Question 8

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

Accepted Answer

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

Question 9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$3 - x ^ { 2 } - 72$

Accepted Answer

A)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 8 \right)$ 
B)  $\left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 72 \right)$ 
C)  $\left( x ^ { 2 } + 8 \right) \left( x ^ { 2 } - 9 \right)$ 
D)  Prime 
A)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 8 \right)$ 
B)  $\left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 72 \right)$ 
C)  $\left( x ^ { 2 } + 8 \right) \left( x ^ { 2 } - 9 \right)$ 
D)  Prime

Question 10

Choose the polynomial that has the given factor.
-$$3 x + 5$$

Accepted Answer

A)  $3 x ^ { 2 } - 16 x - 35$ 
B)  $3 x ^ { 2 } + 16 x + 35$ 
C)  $x ^ { 2 } - 16 x - 35$ 
D)  $3 x ^ { 2 } + 16 x - 35$ 
A)  $3 x ^ { 2 } - 16 x - 35$ 
B)  $3 x ^ { 2 } + 16 x + 35$ 
C)  $x ^ { 2 } - 16 x - 35$ 
D)  $3 x ^ { 2 } + 16 x - 35$

Question 11

Find the GCF.
-$$4 x ^ { 3 } y ^ { 8 } , 16 y ^ { 7 } z ^ { 4 }$$

Accepted Answer

A)  $4 x y z$ 
B)  $2 y ^ { 7 }$ 
C)  $4 y ^ { 7 }$ 
D)  $x ^ { 3 } y ^ { 7 }$ 
A)  $4 x y z$ 
B)  $2 y ^ { 7 }$ 
C)  $4 y ^ { 7 }$ 
D)  $x ^ { 3 } y ^ { 7 }$

Question 12

Factor the GCF out of the given expression.
-$$x ( x - 8 ) - 9 ( x - 8 )$$

Accepted Answer

A)  $( x - 9 ) ( x - 8 )$ 
B)  $( x + 9 ) ( x + 8 )$ 
C)  $( x - 9 ) ( x + 8 )$ 
D)  $( x + 9 ) ( x - 8 )$ 
A)  $( x - 9 ) ( x - 8 )$ 
B)  $( x + 9 ) ( x + 8 )$ 
C)  $( x - 9 ) ( x + 8 )$ 
D)  $( x + 9 ) ( x - 8 )$

Question 13

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-One positive number is 6 less than twice a second number, and their product is 140. Find the two numbers.

Accepted Answer

A)  10   14 
B)  9   12 
C)  11   16 
D)  10   -4 
A)  10   14 
B)  9   12 
C)  11   16 
D)  10   -4

Question 14

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$2 y ^ { 3 } - 128$$

Accepted Answer

A)  $2 ( y - 4 ) \left( y ^ { 2 } + 4 y + 16 \right)$ 
B)  $2 ( y - 4 ) \left( y ^ { 2 } + 16 \right)$ 
C)  $2 ( y + 4 ) \left( y ^ { 2 } - 4 y + 16 \right)$ 
D)  $( 2 y - 4 ) \left( y ^ { 2 } + 4 y + 32 \right)$ 
A)  $2 ( y - 4 ) \left( y ^ { 2 } + 4 y + 16 \right)$ 
B)  $2 ( y - 4 ) \left( y ^ { 2 } + 16 \right)$ 
C)  $2 ( y + 4 ) \left( y ^ { 2 } - 4 y + 16 \right)$ 
D)  $( 2 y - 4 ) \left( y ^ { 2 } + 4 y + 32 \right)$

Question 15

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

Accepted Answer

A)  $( x - 4 ) \left( x ^ { 2 } + 4 x + 16 \right)$ 
B)  $( x - 4 ) \left( x ^ { 2 } + 16 \right)$ 
C)  $( x + 64 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x + 4 ) \left( x ^ { 2 } - 4 x + 16 \right)$ 
A)  $( x - 4 ) \left( x ^ { 2 } + 4 x + 16 \right)$ 
B)  $( x - 4 ) \left( x ^ { 2 } + 16 \right)$ 
C)  $( x + 64 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x + 4 ) \left( x ^ { 2 } - 4 x + 16 \right)$

Question 16

Solve the problem.
-Let $f ( x ) = x ^ { 2 } + 3 x - 108$. Find all values $x$ for which $f ( x ) = 0$.

Accepted Answer

A)  $- 12,9$ 
B)  $- 12,1$ 
C)  12,9 
D)  $12 , - 9$ 
A)  $- 12,9$ 
B)  $- 12,1$ 
C)  12,9 
D)  $12 , - 9$

Question 17

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$9 x ^ { 3 } + 12 x ^ { 2 } + 4 x$$

Accepted Answer

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

Question 18

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$9 x ^ { 2 } + 6 x - 8$$

Accepted Answer

A)  $( 3 x - 2 ) ( 3 x + 4 )$ 
B)  $( 9 x - 2 ) ( x - 8 )$ 
C)  $( 3 x + 2 ) ( 3 x - 4 )$ 
D)  $( 9 x - 2 ) ( x + 4$ 
A)  $( 3 x - 2 ) ( 3 x + 4 )$ 
B)  $( 9 x - 2 ) ( x - 8 )$ 
C)  $( 3 x + 2 ) ( 3 x - 4 )$ 
D)  $( 9 x - 2 ) ( x + 4$

Question 19

Factor the GCF out of the given expression.
-$7 a - 42$

Accepted Answer

A)  $7 ( a + 6 )$ 
B)  $6 ( a - 7 )$ 
C)  $7 ( a - 42 )$ 
D)  $7 ( a - 6 )$ 
A)  $7 ( a + 6 )$ 
B)  $6 ( a - 7 )$ 
C)  $7 ( a - 42 )$ 
D)  $7 ( a - 6 )$

Question 20

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-If a projectile is launched upward from a height of 160 feet at an initial velocity of 144 feet per second, then its height h after t seconds is given by the function h(t) = -16t2 + 144t + 160. After how
Many seconds does the projectile land on the ground?

Accepted Answer

A)  5.0 seconds 
B)  9.0 seconds 
C)  10 seconds 
D)  11 seconds 
A)  5.0 seconds 
B)  9.0 seconds 
C)  10 seconds 
D)  11 seconds

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $5 x ^ { 2 } - 33 x - 56$

Factor the GCF out of the given expression. - $17 x ^ { 8 } + 17 x$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 7 x y + 12 y ^ { 2 }$

Choose the polynomial that has the given factor. -x + 7

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $5 x ^ { 5 } + 10 x ^ { 4 } y - 75 x ^ { 3 } y ^ { 2 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $24 x ^ { 6 } + 66 x ^ { 4 } + 45 x ^ { 2 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 4 x - 45$

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

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $3 - x ^ { 2 } - 72$

Choose the polynomial that has the given factor. - $3 x + 5$

Find the GCF. - $4 x ^ { 3 } y ^ { 8 } , 16 y ^ { 7 } z ^ { 4 }$

Factor the GCF out of the given expression. - $x ( x - 8 ) - 9 ( x - 8 )$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -One positive number is 6 less than twice a second number, and their product is 140. Find the two numbers.

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $2 y ^ { 3 } - 128$

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

Solve the problem. -Let $f ( x ) = x ^ { 2 } + 3 x - 108$ . Find all values $x$ for which $f ( x ) = 0$ .

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $9 x ^ { 3 } + 12 x ^ { 2 } + 4 x$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $9 x ^ { 2 } + 6 x - 8$

Factor the GCF out of the given expression. - $7 a - 42$

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 completely. If the polynomial cannot be factored, write ʺprime.ʺ - 5x2−33x−565 x ^ { 2 } - 33 x - 565x2−33x−56

Factor the GCF out of the given expression. - 17x8+17x17 x ^ { 8 } + 17 x17x8+17x

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - x2−7xy+12y2x ^ { 2 } - 7 x y + 12 y ^ { 2 }x2−7xy+12y2