Question 1

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$5 x ^ { 2 } + 5 x y - 60 y ^ { 2 }$

Accepted Answer

A)  $( 5 x + 15 y ) ( x - 4 y )$ 
B)  $5 ( x + 3 y ) ( x - 4 y )$ 
C)  $( x - 3 y ) ( 5 x + 20 y )$ 
D)  $5 ( x - 3 y ) ( x + 4 y )$ 
A)  $( 5 x + 15 y ) ( x - 4 y )$ 
B)  $5 ( x + 3 y ) ( x - 4 y )$ 
C)  $( x - 3 y ) ( 5 x + 20 y )$ 
D)  $5 ( x - 3 y ) ( x + 4 y )$

Question 2

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

Accepted Answer

A)  $( 4 x + 3 ) ( x + 3 )$ 
B)  $( 2 x - 3 ) ( 2 x - 3 )$ 
C)  $( 4 x + 1 ) ( x - 9 )$ 
D)  $( 2 x + 3 ) ( 2 x + 3 )$ 
A)  $( 4 x + 3 ) ( x + 3 )$ 
B)  $( 2 x - 3 ) ( 2 x - 3 )$ 
C)  $( 4 x + 1 ) ( x - 9 )$ 
D)  $( 2 x + 3 ) ( 2 x + 3 )$

Question 3

Find the GCF.
-$88 x ^ { 2 } , 44 x ^ { 6 }$

Accepted Answer

A)  $88 x ^ { 2 }$ 
B)  $44 x ^ { 2 }$ 
C)  $22 \mathrm { x } ^ { 4 }$ 
D)  $66 \mathrm { x } ^ { 2 }$ 
A)  $88 x ^ { 2 }$ 
B)  $44 x ^ { 2 }$ 
C)  $22 \mathrm { x } ^ { 4 }$ 
D)  $66 \mathrm { x } ^ { 2 }$

Question 4

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The height of a triangle is 4 centimeters more than the base. If the area of the triangle is 198 square centimeters, find the base and height of the triangle.

Accepted Answer

A)  Base: 14 centimeters; Height: 18 centimeters 
B)  Base: 18 centimeters; Height: 22 centimeters 
C)  Base: 17 centimeters; Height: 23 centimeters 
D)  Base: 17 centimeters; Height: 21 centimeters 
A)  Base: 14 centimeters; Height: 18 centimeters 
B)  Base: 18 centimeters; Height: 22 centimeters 
C)  Base: 17 centimeters; Height: 23 centimeters 
D)  Base: 17 centimeters; Height: 21 centimeters

Question 5

Factor by grouping.
-$$4 x ^ { 2 } - 20 x - 28 x + 140$$

Accepted Answer

A)  $( x - 5 ) ( 4 x - 28 )$ 
B)  $4 ( x + 5 ) ( x + 7 )$ 
C)  $4 ( x - 5 ) ( x - 7 )$ 
D)  $( x - 5 ) ( x - 7 )$ 
A)  $( x - 5 ) ( 4 x - 28 )$ 
B)  $4 ( x + 5 ) ( x + 7 )$ 
C)  $4 ( x - 5 ) ( x - 7 )$ 
D)  $( x - 5 ) ( x - 7 )$

Question 6

Factor by grouping.
-$$x ^ { 3 } + 8 x ^ { 2 } + 5 x + 40$$

Accepted Answer

A)  $\left( x ^ { 2 } + 5 \right) ( x + 8 )$ 
B)  $\left( x ^ { 2 } + 5 \right) ( x - 8 )$ 
C)  $\left( x ^ { 2 } + 5 \right) ( x + 8 x )$ 
D)  $\left( x ^ { 3 } + 5 \right) ( x + 8 )$ 
A)  $\left( x ^ { 2 } + 5 \right) ( x + 8 )$ 
B)  $\left( x ^ { 2 } + 5 \right) ( x - 8 )$ 
C)  $\left( x ^ { 2 } + 5 \right) ( x + 8 x )$ 
D)  $\left( x ^ { 3 } + 5 \right) ( x + 8 )$

Question 7

Determine which factoring technique is appropriate for the given polynomial.
-$$x ^ { 2 } + 13 x + 40$$

Accepted Answer

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

Question 8

Find the GCF.
-$x y ^ { 6 } , x y ^ { 5 }$

Accepted Answer

A)  $y ^ { 5 }$ 
B)  $x ^ { 7 } y ^ { 6 }$ 
C)  $x ^ { 7 } y ^ { 5 }$ 
D)  $x y ^ { 5 }$ 
A)  $y ^ { 5 }$ 
B)  $x ^ { 7 } y ^ { 6 }$ 
C)  $x ^ { 7 } y ^ { 5 }$ 
D)  $x y ^ { 5 }$

Question 9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$64 g ^ { 3 } + 125 h ^ { 3 }$$

Accepted Answer

A)  $( 4 \mathrm {~g} + 5 \mathrm {~h} ) \left( 16 \mathrm {~g} ^ { 2 } - 20 \mathrm { gh } + 25 \mathrm {~h} ^ { 2 } \right)$ 
B)  $( 4 g - 5 h ) \left( 16 g ^ { 2 } + 25 h ^ { 2 } \right)$ 
C)  $\left( 4 g + 5 h ^ { 2 } \right) \left( 16 g ^ { 2 } - 20 g h + 25 h ^ { 2 } \right)$ 
D)  $( 4 g - 5 h ) \left( 16 g ^ { 2 } + 20 g h + 25 h ^ { 2 } \right)$ 
A)  $( 4 \mathrm {~g} + 5 \mathrm {~h} ) \left( 16 \mathrm {~g} ^ { 2 } - 20 \mathrm { gh } + 25 \mathrm {~h} ^ { 2 } \right)$ 
B)  $( 4 g - 5 h ) \left( 16 g ^ { 2 } + 25 h ^ { 2 } \right)$ 
C)  $\left( 4 g + 5 h ^ { 2 } \right) \left( 16 g ^ { 2 } - 20 g h + 25 h ^ { 2 } \right)$ 
D)  $( 4 g - 5 h ) \left( 16 g ^ { 2 } + 20 g h + 25 h ^ { 2 } \right)$

Question 10

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-Use Gauss's function, $f ( n ) = \frac { 1 } { 2 } n ^ { 2 } + \frac { 1 } { 2 } n$, to find a natural number $n$ such that the sum of the first $n$ natural numbers is 378 .

Accepted Answer

A)  27 
B)  29 
C)  28 
D)  26 
A)  27 
B)  29 
C)  28 
D)  26

Question 11

Determine which factoring technique is appropriate for the given polynomial.
-$$x ^ { 2 } + 121$$

Accepted Answer

A)  sum of cubes 
B)  factoring by grouping 
C)  factor out GCF 
D)  sum of squares 
A)  sum of cubes 
B)  factoring by grouping 
C)  factor out GCF 
D)  sum of squares

Question 12

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

Accepted Answer

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

Question 13

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$27 x ^ { 2 } - 117 x - 90$

Accepted Answer

A)  $( 27 x + 18 ) ( x - 5 )$ 
B)  $9 ( 3 x - 2 ) ( x + 5 )$ 
C)  $9 ( 3 x + 2 ) ( x - 5 )$ 
D)  $( 3 x + 2 ) ( 9 x - 45 )$ 
A)  $( 27 x + 18 ) ( x - 5 )$ 
B)  $9 ( 3 x - 2 ) ( x + 5 )$ 
C)  $9 ( 3 x + 2 ) ( x - 5 )$ 
D)  $( 3 x + 2 ) ( 9 x - 45 )$

Question 14

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$169 \mathrm { k } ^ { 2 } - 36 \mathrm {~m} ^ { 2 }$

Accepted Answer

A)  $( 13 k + 6 m ) ^ { 2 }$ 
B)  $( 13 k + 6 m ) ( 13 k - 6 m )$ 
C)  $( 13 k - 6 m ) ^ { 2 }$ 
D)  $( 169 \mathrm { k } + \mathrm { m } ) ( \mathrm { k } - 36 \mathrm {~m} )$ 
A)  $( 13 k + 6 m ) ^ { 2 }$ 
B)  $( 13 k + 6 m ) ( 13 k - 6 m )$ 
C)  $( 13 k - 6 m ) ^ { 2 }$ 
D)  $( 169 \mathrm { k } + \mathrm { m } ) ( \mathrm { k } - 36 \mathrm {~m} )$

Question 15

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 4 } - 11 x ^ { 3 } + 30 x ^ { 2 }$$

Accepted Answer

A)  $x ^ { 2 } ( x + 5 ) ( x + 6 )$ 
B)  $\left( x ^ { 2 } - 5 \right) \left( x ^ { 2 } - 6 \right)$ 
C)  $x ^ { 2 } ( x - 5 ) ( x - 6 )$ 
D)  $x ^ { 2 } ( x - 30 ) ( x - 1 )$ 
A)  $x ^ { 2 } ( x + 5 ) ( x + 6 )$ 
B)  $\left( x ^ { 2 } - 5 \right) \left( x ^ { 2 } - 6 \right)$ 
C)  $x ^ { 2 } ( x - 5 ) ( x - 6 )$ 
D)  $x ^ { 2 } ( x - 30 ) ( x - 1 )$

Question 16

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } - 10 x + 16$$

Accepted Answer

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

Question 17

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } + 8 x - 20$$

Accepted Answer

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

Question 18

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-Use Gauss's function, $f ( n ) = \frac { 1 } { 2 } n ^ { 2 } + \frac { 1 } { 2 } n$, to find a natural number $n$ such that the sum of the first $n$ natural numbers is 10 .

Accepted Answer

A)  6 
B)  3 
C)  5 
D)  4 
A)  6 
B)  3 
C)  5 
D)  4

Question 19

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$125 \mathrm { x } ^ { 12 } + 8 \mathrm { y } ^ { 9 }$

Accepted Answer

A)  $\left( 5 x ^ { 4 } + 2 y ^ { 3 } \right) \left( 25 x ^ { 8 } + 10 x ^ { 4 } y ^ { 3 } + 4 y ^ { 6 } \right)$ 
B)  $\left( 5 x ^ { 4 } - 2 y ^ { 3 } \right) \left( 5 x ^ { 4 } + 2 y ^ { 3 } \right)$ 
C)  $\left( 5 x ^ { 4 } - 2 y ^ { 3 } \right) \left( 25 x ^ { 2 } + 10 x ^ { 4 } y ^ { 3 } + 4 y ^ { 6 } b ^ { 2 } \right)$ 
D)  $\left( 5 x ^ { 4 } + 2 y ^ { 3 } \right) \left( 25 x ^ { 8 } - 10 x ^ { 4 } y ^ { 3 } + 4 y ^ { 6 } \right)$ 
A)  $\left( 5 x ^ { 4 } + 2 y ^ { 3 } \right) \left( 25 x ^ { 8 } + 10 x ^ { 4 } y ^ { 3 } + 4 y ^ { 6 } \right)$ 
B)  $\left( 5 x ^ { 4 } - 2 y ^ { 3 } \right) \left( 5 x ^ { 4 } + 2 y ^ { 3 } \right)$ 
C)  $\left( 5 x ^ { 4 } - 2 y ^ { 3 } \right) \left( 25 x ^ { 2 } + 10 x ^ { 4 } y ^ { 3 } + 4 y ^ { 6 } b ^ { 2 } \right)$ 
D)  $\left( 5 x ^ { 4 } + 2 y ^ { 3 } \right) \left( 25 x ^ { 8 } - 10 x ^ { 4 } y ^ { 3 } + 4 y ^ { 6 } \right)$

Question 20

Solve the problem.
-Let $f ( x ) = x ^ { 2 } + 15 x$. Find all values $x$ for which $f ( x ) = - 54$.

Accepted Answer

A)  $0 , - 54$ 
B)  9,6 
C)  $- \frac { 5 } { 18 } , - \frac { 1 } { 54 }$ 
D)  $- 9 , - 6$ 
A)  $0 , - 54$ 
B)  9,6 
C)  $- \frac { 5 } { 18 } , - \frac { 1 } { 54 }$ 
D)  $- 9 , - 6$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $5 x ^ { 2 } + 5 x y - 60 y ^ { 2 }$

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

Find the GCF. - $88 x ^ { 2 } , 44 x ^ { 6 }$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The height of a triangle is 4 centimeters more than the base. If the area of the triangle is 198 square centimeters, find the base and height of the triangle.

Factor by grouping. - $4 x ^ { 2 } - 20 x - 28 x + 140$

Factor by grouping. - $x ^ { 3 } + 8 x ^ { 2 } + 5 x + 40$

Determine which factoring technique is appropriate for the given polynomial. - $x ^ { 2 } + 13 x + 40$

Find the GCF. - $x y ^ { 6 } , x y ^ { 5 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $64 g ^ { 3 } + 125 h ^ { 3 }$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -Use Gauss's function, $f ( n ) = \frac { 1 } { 2 } n ^ { 2 } + \frac { 1 } { 2 } n$ , to find a natural number $n$ such that the sum of the first $n$ natural numbers is 378 .

Determine which factoring technique is appropriate for the given polynomial. - $x ^ { 2 } + 121$

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

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $27 x ^ { 2 } - 117 x - 90$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $169 \mathrm { k } ^ { 2 } - 36 \mathrm {~m} ^ { 2 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 4 } - 11 x ^ { 3 } + 30 x ^ { 2 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 10 x + 16$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } + 8 x - 20$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -Use Gauss's function, $f ( n ) = \frac { 1 } { 2 } n ^ { 2 } + \frac { 1 } { 2 } n$ , to find a natural number $n$ such that the sum of the first $n$ natural numbers is 10 .

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $125 \mathrm { x } ^ { 12 } + 8 \mathrm { y } ^ { 9 }$

Solve the problem. -Let $f ( x ) = x ^ { 2 } + 15 x$ . Find all values $x$ for which $f ( x ) = - 54$ .

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+5xy−60y25 x ^ { 2 } + 5 x y - 60 y ^ { 2 }5x2+5xy−60y2

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 4x2+12x+94 x ^ { 2 } + 12 x + 94x2+12x+9

Find the GCF. - 88x2,44x688 x ^ { 2 } , 44 x ^ { 6 }88x2,44x6

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The height of a triangle is 4 centimeters more than the base. If the area of the triangle is 198 square centimeters, find the base and height of the triangle.

Factor by grouping. - 4x2−20x−28x+1404 x ^ { 2 } - 20 x - 28 x + 1404x2−20x−28x+140

Factor by grouping. - x3+8x2+5x+40x ^ { 3 } + 8 x ^ { 2 } + 5 x + 40x3+8x2+5x+40

Determine which factoring technique is appropriate for the given polynomial. - x2+13x+40x ^ { 2 } + 13 x + 40x2+13x+40

Find the GCF. - xy6,xy5x y ^ { 6 } , x y ^ { 5 }xy6,xy5

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 64g3+125h364 g ^ { 3 } + 125 h ^ { 3 }64g3+125h3

Determine which factoring technique is appropriate for the given polynomial. - x2+121x ^ { 2 } + 121x2+121

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - x4−81x ^ { 4 } - 81x4−81

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 27x2−117x−9027 x ^ { 2 } - 117 x - 9027x2−117x−90

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 169k2−36 m2169 \mathrm { k } ^ { 2 } - 36 \mathrm {~m} ^ { 2 }169k2−36 m2

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - x4−11x3+30x2x ^ { 4 } - 11 x ^ { 3 } + 30 x ^ { 2 }x4−11x3+30x2

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - x2−10x+16x ^ { 2 } - 10 x + 16x2−10x+16

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - x2+8x−20x ^ { 2 } + 8 x - 20x2+8x−20

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 125x12+8y9125 \mathrm { x } ^ { 12 } + 8 \mathrm { y } ^ { 9 }125x12+8y9

Solve the problem. -Let f(x)=x2+15xf ( x ) = x ^ { 2 } + 15 xf(x)=x2+15x . Find all values xxx for which f(x)=−54f ( x ) = - 54f(x)=−54 .