Question 1

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 3 } + 4 x ^ { 2 } - 77 x$$

Accepted Answer

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

Question 2

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The difference of two positive numbers is 6 and their product is 187. Find the two numbers

Accepted Answer

A)  10   16 
B)  14   20 
C)  21   27 
D)  11   17 
A)  10   16 
B)  14   20 
C)  21   27 
D)  11   17 D

Question 3

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-A rectangular garden has dimensions of 22 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 564 square feet?

Accepted Answer

A)  8 feet 
B)  6 feet 
C)  8.5 feet 
D)  7 feet 
A)  8 feet 
B)  6 feet 
C)  8.5 feet 
D)  7 feet B

Question 4

Find the GCF.
-$\mathrm { p } ^ { 3 } \mathrm { q } ^ { 5 } \mathrm { r } , \mathrm { p } ^ { 6 } \mathrm { q } ^ { 2 } \mathrm { r } ^ { 4 }$

Accepted Answer

A)  $p ^ { 3 } q ^ { 3 } r ^ { 3 }$ 
B)  $p ^ { 3 } q ^ { 2 } r ^ { 4 }$ 
C)  $p ^ { 3 } q ^ { 2 } r$ 
D)  $\mathrm { p } ^ { 3 } \mathrm { q } ^ { 2 }$ 
A)  $p ^ { 3 } q ^ { 3 } r ^ { 3 }$ 
B)  $p ^ { 3 } q ^ { 2 } r ^ { 4 }$ 
C)  $p ^ { 3 } q ^ { 2 } r$ 
D)  $\mathrm { p } ^ { 3 } \mathrm { q } ^ { 2 }$

Question 5

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$2 x ^ { 3 } + 6 x ^ { 2 } - 36 x$$

Accepted Answer

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

Question 6

Factor the GCF out of the given expression.
-$$24 x ^ { 8 } y ^ { 9 } + 16 x ^ { 5 } y ^ { 7 } + 64 x ^ { 2 } y ^ { 5 }$$

Accepted Answer

A)  $8 x ^ { 2 } \left( 3 x ^ { 6 } y ^ { 9 } + 2 x ^ { 3 } y ^ { 7 } + 8 y ^ { 5 } \right)$ 
B)  $x ^ { 2 } \left( 3 x ^ { 6 } y ^ { 9 } + 2 x ^ { 3 } y ^ { 7 } + 8 y ^ { 5 } \right)$ 
C)  $8 x ^ { 2 } y ^ { 5 } \left( 3 x ^ { 6 } y ^ { 4 } + 2 x ^ { 3 } y ^ { 2 } + 8 \right)$ 
D)  $8 \left( 3 x ^ { 8 } y ^ { 9 } + 2 x ^ { 5 } y ^ { 7 } + 8 x ^ { 2 } y ^ { 5 } \right)$ 
A)  $8 x ^ { 2 } \left( 3 x ^ { 6 } y ^ { 9 } + 2 x ^ { 3 } y ^ { 7 } + 8 y ^ { 5 } \right)$ 
B)  $x ^ { 2 } \left( 3 x ^ { 6 } y ^ { 9 } + 2 x ^ { 3 } y ^ { 7 } + 8 y ^ { 5 } \right)$ 
C)  $8 x ^ { 2 } y ^ { 5 } \left( 3 x ^ { 6 } y ^ { 4 } + 2 x ^ { 3 } y ^ { 2 } + 8 \right)$ 
D)  $8 \left( 3 x ^ { 8 } y ^ { 9 } + 2 x ^ { 5 } y ^ { 7 } + 8 x ^ { 2 } y ^ { 5 } \right)$

Question 7

Find the GCF.
-$s ^ { 5 } t ^ { 4 } , s ^ { 2 } t ^ { 6 }$

Accepted Answer

A)  $s ^ { 7 } t ^ { 6 }$ 
B)  $s ^ { 2 } t ^ { 2 }$ 
C)  $\mathrm { s } ^ { 2 } \mathrm { t } ^ { 4 }$ 
D)  $s ^ { 5 } t ^ { 4 }$ 
A)  $s ^ { 7 } t ^ { 6 }$ 
B)  $s ^ { 2 } t ^ { 2 }$ 
C)  $\mathrm { s } ^ { 2 } \mathrm { t } ^ { 4 }$ 
D)  $s ^ { 5 } t ^ { 4 }$

Question 8

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$16 x ^ { 2 } - 24 x + 9$$

Accepted Answer

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

Question 9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$4 x ^ { 2 } - 7 x + 6$$

Accepted Answer

A)  prime 
B)  $( 4 x - 6 ) ( x - 1 )$ 
C)  $( 2 x - 6 ) ( 2 x - 1 )$ 
D)  $( 4 x - 1 ) ( x - 6 )$ 
A)  prime 
B)  $( 4 x - 6 ) ( x - 1 )$ 
C)  $( 2 x - 6 ) ( 2 x - 1 )$ 
D)  $( 4 x - 1 ) ( x - 6 )$

Question 10

Find the GCF.
-16,20

Accepted Answer

A)  16 
B)  1 
C)  4 
D)  2 
A)  16 
B)  1 
C)  4 
D)  2

Question 11

Determine which factoring technique is appropriate for the given polynomial.
-$$x ^ { 3 } - 7 x ^ { 2 } - 5 x + 35$$

Accepted Answer

A)  difference of squares 
B)  factoring by grouping 
C)  sum of cubes 
D)  difference of cubes 
A)  difference of squares 
B)  factoring by grouping 
C)  sum of cubes 
D)  difference of cubes

Question 12

Solve the problem.
-Let $f ( x ) = 3 x ^ { 2 } - 18 x + 24$. Find all values $x$ for which $f ( x ) = 0$.

Accepted Answer

A)  2,4 
B)  $- 2 , - 4$ 
C)  $3,2,4$ 
D)  $0,2,4$ 
A)  2,4 
B)  $- 2 , - 4$ 
C)  $3,2,4$ 
D)  $0,2,4$

Question 13

Factor the GCF out of the given expression.
-$40 m ^ { 8 } - 24 m ^ { 4 } + 28 m ^ { 2 }$

Accepted Answer

A)  $m ^ { 2 } \left( 40 m ^ { 6 } - 24 m ^ { 2 } + 28 \right)$ 
B)  $4 \left( 10 m ^ { 8 } - 6 m ^ { 4 } + 7 m ^ { 2 } \right)$ 
C)  $4 m \left( 10 m ^ { 8 } - 6 m ^ { 4 } + 7 m ^ { 2 } \right)$ 
D)  $4 m ^ { 2 } \left( 10 m ^ { 6 } - 6 m ^ { 2 } + 7 \right)$ 
A)  $m ^ { 2 } \left( 40 m ^ { 6 } - 24 m ^ { 2 } + 28 \right)$ 
B)  $4 \left( 10 m ^ { 8 } - 6 m ^ { 4 } + 7 m ^ { 2 } \right)$ 
C)  $4 m \left( 10 m ^ { 8 } - 6 m ^ { 4 } + 7 m ^ { 2 } \right)$ 
D)  $4 m ^ { 2 } \left( 10 m ^ { 6 } - 6 m ^ { 2 } + 7 \right)$

Question 14

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$16 x ^ { 2 } + 49$

Accepted Answer

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

Question 15

Find the GCF.
-152,304

Accepted Answer

A)  8 
B)  152 
C)  76 
D)  19 
A)  8 
B)  152 
C)  76 
D)  19

Question 16

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } - 3 x - 108$$

Accepted Answer

A)  $( x - 108 ) ( x + 1 )$ 
B)  $( x + 9 ) ( x - 12 )$ 
C)  $( x - 9 ) ( x + 12 )$ 
D)  Prime 
A)  $( x - 108 ) ( x + 1 )$ 
B)  $( x + 9 ) ( x - 12 )$ 
C)  $( x - 9 ) ( x + 12 )$ 
D)  Prime

Question 17

Find the GCF.
-$14 x ^ { 5 } y ^ { 2 } , 56 x ^ { 8 } y , 196 x ^ { 6 } y ^ { 5 } z$

Accepted Answer

A)  $14 x ^ { 5 } y$ 
B)  $784 x ^ { 3 }$ 
C)  $14 x ^ { 3 } y ^ { 5 } z$ 
D)  $56 \mathrm { x } ^ { 5 } \mathrm { z }$ 
A)  $14 x ^ { 5 } y$ 
B)  $784 x ^ { 3 }$ 
C)  $14 x ^ { 3 } y ^ { 5 } z$ 
D)  $56 \mathrm { x } ^ { 5 } \mathrm { z }$

Question 18

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$16 x ^ { 2 } + 81$$

Accepted Answer

A)  $( 4 x - 9 ) ^ { 2 }$ 
B)  prime 
C)  $( 4 x + 9 ) ^ { 2 }$ 
D)  $( 4 x + 9 ) ( 4 x - 9 )$ 
A)  $( 4 x - 9 ) ^ { 2 }$ 
B)  prime 
C)  $( 4 x + 9 ) ^ { 2 }$ 
D)  $( 4 x + 9 ) ( 4 x - 9 )$

Question 19

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 5 } + 2 x ^ { 4 } - 99 x ^ { 3 }$$

Accepted Answer

A)  $\left( x ^ { 4 } + 11 x ^ { 3 } \right) ( x - 9 )$ 
B)  $\left( x ^ { 2 } - 11 \right) \left( x ^ { 3 } + 9 \right)$ 
C)  $x ^ { 3 } ( x + 11 ) ( x - 9 )$ 
D)  $x ^ { 3 } ( x - 11 ) ( x + 9 )$ 
A)  $\left( x ^ { 4 } + 11 x ^ { 3 } \right) ( x - 9 )$ 
B)  $\left( x ^ { 2 } - 11 \right) \left( x ^ { 3 } + 9 \right)$ 
C)  $x ^ { 3 } ( x + 11 ) ( x - 9 )$ 
D)  $x ^ { 3 } ( x - 11 ) ( x + 9 )$

Question 20

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-x6 - 8

Accepted Answer

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

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 3 } + 4 x ^ { 2 } - 77 x$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The difference of two positive numbers is 6 and their product is 187. Find the two numbers

Find the GCF. - $\mathrm { p } ^ { 3 } \mathrm { q } ^ { 5 } \mathrm { r } , \mathrm { p } ^ { 6 } \mathrm { q } ^ { 2 } \mathrm { r } ^ { 4 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $2 x ^ { 3 } + 6 x ^ { 2 } - 36 x$

Factor the GCF out of the given expression. - $24 x ^ { 8 } y ^ { 9 } + 16 x ^ { 5 } y ^ { 7 } + 64 x ^ { 2 } y ^ { 5 }$

Find the GCF. - $s ^ { 5 } t ^ { 4 } , s ^ { 2 } t ^ { 6 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $16 x ^ { 2 } - 24 x + 9$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $4 x ^ { 2 } - 7 x + 6$

Find the GCF. -16,20

Determine which factoring technique is appropriate for the given polynomial. - $x ^ { 3 } - 7 x ^ { 2 } - 5 x + 35$

Solve the problem. -Let $f ( x ) = 3 x ^ { 2 } - 18 x + 24$ . Find all values $x$ for which $f ( x ) = 0$ .

Factor the GCF out of the given expression. - $40 m ^ { 8 } - 24 m ^ { 4 } + 28 m ^ { 2 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $16 x ^ { 2 } + 49$

Find the GCF. -152,304

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 3 x - 108$

Find the GCF. - $14 x ^ { 5 } y ^ { 2 } , 56 x ^ { 8 } y , 196 x ^ { 6 } y ^ { 5 } z$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $16 x ^ { 2 } + 81$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 5 } + 2 x ^ { 4 } - 99 x ^ { 3 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ -x⁶ - 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 completely. If the polynomial cannot be factored, write ʺprime.ʺ - x3+4x2−77xx ^ { 3 } + 4 x ^ { 2 } - 77 xx3+4x2−77x

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The difference of two positive numbers is 6 and their product is 187. Find the two numbers

Find the GCF. - p3q5r,p6q2r4\mathrm { p } ^ { 3 } \mathrm { q } ^ { 5 } \mathrm { r } , \mathrm { p } ^ { 6 } \mathrm { q } ^ { 2 } \mathrm { r } ^ { 4 }p3q5r,p6q2r4

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 2x3+6x2−36x2 x ^ { 3 } + 6 x ^ { 2 } - 36 x2x3+6x2−36x

Factor the GCF out of the given expression. - 24x8y9+16x5y7+64x2y524 x ^ { 8 } y ^ { 9 } + 16 x ^ { 5 } y ^ { 7 } + 64 x ^ { 2 } y ^ { 5 }24x8y9+16x5y7+64x2y5

Find the GCF. - s5t4,s2t6s ^ { 5 } t ^ { 4 } , s ^ { 2 } t ^ { 6 }s5t4,s2t6

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 16x2−24x+916 x ^ { 2 } - 24 x + 916x2−24x+9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 4x2−7x+64 x ^ { 2 } - 7 x + 64x2−7x+6