Question 1

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$2 x ^ { 2 } - 12 x + 10$$

Accepted Answer

A)  $2 ( x - 1 ) ( x - 10 )$ 
B)  $2 ( x + 5 ) ( x + 1 )$ 
C)  $2 ( x - 5 ) ( x - 1 )$ 
D)  $( 2 x - 1 ) ( x - 10 )$ 
A)  $2 ( x - 1 ) ( x - 10 )$ 
B)  $2 ( x + 5 ) ( x + 1 )$ 
C)  $2 ( x - 5 ) ( x - 1 )$ 
D)  $( 2 x - 1 ) ( x - 10 )$

Question 2

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$18 x ^ { 3 } - 78 x ^ { 2 } - 60 x$$

Accepted Answer

A)  $6 ( 3 x - 2 ) ( x + 5 )$ 
B)  $x ( 3 x + 2 ) ( 6 x - 30 )$ 
C)  $\left( x ^ { 2 } - 5 \right) ( 18 x + 12 )$ 
D)  $6 x ( 3 x + 2 ) ( x - 5 )$ 
A)  $6 ( 3 x - 2 ) ( x + 5 )$ 
B)  $x ( 3 x + 2 ) ( 6 x - 30 )$ 
C)  $\left( x ^ { 2 } - 5 \right) ( 18 x + 12 )$ 
D)  $6 x ( 3 x + 2 ) ( x - 5 )$

Question 3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$y z ^ { 3 } + 512 y$$

Accepted Answer

A)  $( y z + 8 ) \left( z ^ { 2 } - 8 z + 64 y \right)$ 
B)  $y ( z + 8 ) \left( z ^ { 2 } + 64 \right)$ 
C)  $y ( z - 8 ) \left( z ^ { 2 } + 8 z + 64 \right)$ 
D)  $y ( z + 8 ) \left( z ^ { 2 } - 8 z + 64 \right)$ 
A)  $( y z + 8 ) \left( z ^ { 2 } - 8 z + 64 y \right)$ 
B)  $y ( z + 8 ) \left( z ^ { 2 } + 64 \right)$ 
C)  $y ( z - 8 ) \left( z ^ { 2 } + 8 z + 64 \right)$ 
D)  $y ( z + 8 ) \left( z ^ { 2 } - 8 z + 64 \right)$

Question 4

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$1000 p ^ { 3 } - 1$

Accepted Answer

A)  $( 10 p - 1 ) \left( 100 p ^ { 2 } + 1 \right)$ 
B)  $( 10 p + 1 ) \left( 100 p ^ { 2 } - 10 p + 1 \right)$ 
C)  $( 1000 p - 1 ) \left( p ^ { 2 } + 10 p + 1 \right)$ 
D)  $( 10 p - 1 ) \left( 100 p ^ { 2 } + 10 p + 1 \right)$ 
A)  $( 10 p - 1 ) \left( 100 p ^ { 2 } + 1 \right)$ 
B)  $( 10 p + 1 ) \left( 100 p ^ { 2 } - 10 p + 1 \right)$ 
C)  $( 1000 p - 1 ) \left( p ^ { 2 } + 10 p + 1 \right)$ 
D)  $( 10 p - 1 ) \left( 100 p ^ { 2 } + 10 p + 1 \right)$

Question 5

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$c ^ { 3 } - 512 d ^ { 3 }$$

Accepted Answer

A)  $( c + 8 d ) \left( c ^ { 2 } - 8 c d + 64 d ^ { 2 } \right)$ 
B)  $( c - 8 d ) \left( c ^ { 2 } + 8 c d + 64 d ^ { 2 } \right)$ 
C)  $\left( \mathrm { c } + 512 \mathrm {~d} ^ { 3 } \right) \left( \mathrm { c } ^ { 2 } - 1 \right)$ 
D)  $( c - 8 d ) \left( c ^ { 2 } + 64 d ^ { 2 } \right)$ 
A)  $( c + 8 d ) \left( c ^ { 2 } - 8 c d + 64 d ^ { 2 } \right)$ 
B)  $( c - 8 d ) \left( c ^ { 2 } + 8 c d + 64 d ^ { 2 } \right)$ 
C)  $\left( \mathrm { c } + 512 \mathrm {~d} ^ { 3 } \right) \left( \mathrm { c } ^ { 2 } - 1 \right)$ 
D)  $( c - 8 d ) \left( c ^ { 2 } + 64 d ^ { 2 } \right)$

Question 6

Find the GCF.
-40,31

Accepted Answer

A)  4 
B)  1 
C)  10 
D)  31 
A)  4 
B)  1 
C)  10 
D)  31

Question 7

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$25 x ^ { 5 } - 9 x$

Accepted Answer

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

Question 8

Determine which factoring technique is appropriate for the given polynomial.
-$$x ^ { 2 } - 4$$

Accepted Answer

A)  difference of squares 
B)  difference of cubes 
C)  sum of squares 
D)  factor out GCF 
A)  difference of squares 
B)  difference of cubes 
C)  sum of squares 
D)  factor out GCF

Question 9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$4 x ^ { 2 } + 4 x + 1$$

Accepted Answer

A)  $( 2 x - 1 ) ^ { 2 }$ 
B)  $( 2 x + 1 ) ^ { 2 }$ 
C)  prime 
D)  $( 2 x - 1 ) ( 2 x + 1 )$ 
A)  $( 2 x - 1 ) ^ { 2 }$ 
B)  $( 2 x + 1 ) ^ { 2 }$ 
C)  prime 
D)  $( 2 x - 1 ) ( 2 x + 1 )$

Question 10

Factor the GCF out of the given expression.
-$$8 x ( x - 6 ) - ( x - 6 )$$

Accepted Answer

A)  $8 x ( x - 6 )$ 
B)  $( 8 x - 6 ) ( x - 1 )$ 
C)  $( 8 x + 6 ) ( x - 1 )$ 
D)  $( 8 x - 1 ) ( x - 6 )$ 
A)  $8 x ( x - 6 )$ 
B)  $( 8 x - 6 ) ( x - 1 )$ 
C)  $( 8 x + 6 ) ( x - 1 )$ 
D)  $( 8 x - 1 ) ( x - 6 )$

Question 11

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$m ^ { 5 } - 625 m$$

Accepted Answer

A)  $m \left( m ^ { 2 } + 25 \right) ( m + 5 ) ( m - 5 )$ 
B)  $m \left( m ^ { 2 } + 25 \right) \left( m ^ { 2 } - 25 \right)$ 
C)  $m ( m + 5 ) ^ { 2 } ( m - 5 ) ^ { 2 }$ 
D)  Prime 
A)  $m \left( m ^ { 2 } + 25 \right) ( m + 5 ) ( m - 5 )$ 
B)  $m \left( m ^ { 2 } + 25 \right) \left( m ^ { 2 } - 25 \right)$ 
C)  $m ( m + 5 ) ^ { 2 } ( m - 5 ) ^ { 2 }$ 
D)  Prime

Question 12

Factor the GCF out of the given expression.
-$$9 a ^ { 6 } + 36 a ^ { 4 }$$

Accepted Answer

A)  $a ^ { 4 } \left( 9 a ^ { 2 } + 36 \right)$ 
B)  $9 a ^ { 4 } \left( a ^ { 2 } + 4 \right)$ 
C)  $36 \left( a ^ { 2 } + 4 a \right)$ 
D)  $9 \left( a ^ { 6 } + 4 a ^ { 4 } \right)$ 
A)  $a ^ { 4 } \left( 9 a ^ { 2 } + 36 \right)$ 
B)  $9 a ^ { 4 } \left( a ^ { 2 } + 4 \right)$ 
C)  $36 \left( a ^ { 2 } + 4 a \right)$ 
D)  $9 \left( a ^ { 6 } + 4 a ^ { 4 } \right)$

Question 13

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-A rectangular garden is three times as long as it is wide. If the area of the garden is 2187 square feet, find the length and width of the garden.

Accepted Answer

A)  Length: 27 feet; Width: 3 feet 
B)  Length: 81 feet; Width: 27 feet 
C)  Length: 78 feet; Width: 26 feet 
D)  Length: 729 feet; Width: 3 feet 
A)  Length: 27 feet; Width: 3 feet 
B)  Length: 81 feet; Width: 27 feet 
C)  Length: 78 feet; Width: 26 feet 
D)  Length: 729 feet; Width: 3 feet

Question 14

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and added to the width, the figure becomes a square with an area of 256 square inches. What are the
Dimensions of the original figure?

Accepted Answer

A)  Length: 16 inches; Width: 14 inches 
B)  Length: 16 inches; Width: 12 inches 
C)  Length: 18 inches; Width: 14 inches 
D)  Length:16 inches; Width: 16 inches 
A)  Length: 16 inches; Width: 14 inches 
B)  Length: 16 inches; Width: 12 inches 
C)  Length: 18 inches; Width: 14 inches 
D)  Length:16 inches; Width: 16 inches

Question 15

Factor the GCF out of the given expression.
-$$5 x ^ { 2 } + 30 x$$

Accepted Answer

A)  $5 x ( x + 6 )$ 
B)  $x ( 5 x + 30 )$ 
C)  $5 x ^ { 2 } ( x + 6 )$ 
D)  $5 x ( x + 30 )$ 
A)  $5 x ( x + 6 )$ 
B)  $x ( 5 x + 30 )$ 
C)  $5 x ^ { 2 } ( x + 6 )$ 
D)  $5 x ( x + 30 )$

Question 16

Factor the GCF out of the given expression.
-$$2 x ( 6 x - 5 ) - 3 ( 6 x - 5 )$$

Accepted Answer

A)  $( 12 x + 3 ) ( x + 5 )$ 
B)  $( 6 x + 5 ) ( 2 x + 3 )$ 
C)  $( 12 x - 3 ) ( x - 5 )$ 
D)  $( 6 x - 5 ) ( 2 x - 3 )$ 
A)  $( 12 x + 3 ) ( x + 5 )$ 
B)  $( 6 x + 5 ) ( 2 x + 3 )$ 
C)  $( 12 x - 3 ) ( x - 5 )$ 
D)  $( 6 x - 5 ) ( 2 x - 3 )$

Question 17

Factor the GCF out of the given expression.
-$72 x ^ { 9 } y ^ { 9 } - 108 x ^ { 5 } y ^ { 4 } + 24 x ^ { 7 } y ^ { 2 }$

Accepted Answer

A)  $12 \left( 6 x ^ { 9 } y ^ { 9 } - 9 x ^ { 5 } y ^ { 4 } + 2 x ^ { 7 } y ^ { 2 } \right)$ 
B)  $12 x \left( 6 x ^ { 9 } y ^ { 9 } - 9 x ^ { 5 } y ^ { 4 } + 2 x ^ { 7 } y ^ { 2 } \right)$ 
C)  $12 x ^ { 5 } y ^ { 2 } \left( 6 x ^ { 4 } y ^ { 7 } - 9 y ^ { 2 } + 2 x ^ { 2 } \right)$ 
D)  $12 x ^ { 5 } \left( 6 x ^ { 4 } y ^ { 9 } - 9 y ^ { 4 } + 2 x ^ { 2 } y ^ { 2 } \right)$ 
A)  $12 \left( 6 x ^ { 9 } y ^ { 9 } - 9 x ^ { 5 } y ^ { 4 } + 2 x ^ { 7 } y ^ { 2 } \right)$ 
B)  $12 x \left( 6 x ^ { 9 } y ^ { 9 } - 9 x ^ { 5 } y ^ { 4 } + 2 x ^ { 7 } y ^ { 2 } \right)$ 
C)  $12 x ^ { 5 } y ^ { 2 } \left( 6 x ^ { 4 } y ^ { 7 } - 9 y ^ { 2 } + 2 x ^ { 2 } \right)$ 
D)  $12 x ^ { 5 } \left( 6 x ^ { 4 } y ^ { 9 } - 9 y ^ { 4 } + 2 x ^ { 2 } y ^ { 2 } \right)$

Question 18

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 3 } + 1000$$

Accepted Answer

A)  $( x - 10 ) \left( x ^ { 2 } + 10 x + 100 \right)$ 
B)  $( x + 10 ) \left( x ^ { 2 } - 10 x + 100 \right)$ 
C)  $( x + 10 ) \left( x ^ { 2 } + 100 \right)$ 
D)  $( x - 1000 ) \left( x ^ { 2 } - 1 \right)$ 
A)  $( x - 10 ) \left( x ^ { 2 } + 10 x + 100 \right)$ 
B)  $( x + 10 ) \left( x ^ { 2 } - 10 x + 100 \right)$ 
C)  $( x + 10 ) \left( x ^ { 2 } + 100 \right)$ 
D)  $( x - 1000 ) \left( x ^ { 2 } - 1 \right)$

Question 19

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } + 4 x - 21$$

Accepted Answer

A)  $( x - 21 ) ( x + 4 )$ 
B)  $( x - 7 ) ( x + 3 )$ 
C)  $( x + 7 ) ( x - 3 )$ 
D)  Prime 
A)  $( x - 21 ) ( x + 4 )$ 
B)  $( x - 7 ) ( x + 3 )$ 
C)  $( x + 7 ) ( x - 3 )$ 
D)  Prime

Question 20

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } + 8 x y - 128 y ^ { 2 }$$

Accepted Answer

A)  $( x - 16 y ) ( x + 8 y )$ 
B)  $( x + 16 y ) ( x - 8 y )$ 
C)  $( x - y ) ( x + 8 y )$ 
D)  $( x - 16 y ) ( x + y )$ 
A)  $( x - 16 y ) ( x + 8 y )$ 
B)  $( x + 16 y ) ( x - 8 y )$ 
C)  $( x - y ) ( x + 8 y )$ 
D)  $( x - 16 y ) ( x + y )$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $2 x ^ { 2 } - 12 x + 10$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $18 x ^ { 3 } - 78 x ^ { 2 } - 60 x$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $y z ^ { 3 } + 512 y$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $1000 p ^ { 3 } - 1$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $c ^ { 3 } - 512 d ^ { 3 }$

Find the GCF. -40,31

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $25 x ^ { 5 } - 9 x$

Determine which factoring technique is appropriate for the given polynomial. - $x ^ { 2 } - 4$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $4 x ^ { 2 } + 4 x + 1$

Factor the GCF out of the given expression. - $8 x ( x - 6 ) - ( x - 6 )$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $m ^ { 5 } - 625 m$

Factor the GCF out of the given expression. - $9 a ^ { 6 } + 36 a ^ { 4 }$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -A rectangular garden is three times as long as it is wide. If the area of the garden is 2187 square feet, find the length and width of the garden.

Factor the GCF out of the given expression. - $5 x ^ { 2 } + 30 x$

Factor the GCF out of the given expression. - $2 x ( 6 x - 5 ) - 3 ( 6 x - 5 )$

Factor the GCF out of the given expression. - $72 x ^ { 9 } y ^ { 9 } - 108 x ^ { 5 } y ^ { 4 } + 24 x ^ { 7 } y ^ { 2 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 3 } + 1000$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } + 4 x - 21$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } + 8 x y - 128 y ^ { 2 }$

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 - 2x2−12x+102 x ^ { 2 } - 12 x + 102x2−12x+10

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 18x3−78x2−60x18 x ^ { 3 } - 78 x ^ { 2 } - 60 x18x3−78x2−60x

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - yz3+512yy z ^ { 3 } + 512 yyz3+512y

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 1000p3−11000 p ^ { 3 } - 11000p3−1

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - c3−512d3c ^ { 3 } - 512 d ^ { 3 }c3−512d3