Question 1

Find the indicated function value.
-Find $f ( 2 )$ when $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x$.

Accepted Answer

A)  $- 6$ 
B)  26 
C)  6 
D)  42 
A)  $- 6$ 
B)  26 
C)  6 
D)  42

Question 2

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
-$12 a b ^ { 2 } \left( 9 a ^ { 2 } b ^ { 3 } + 10 a b \right)$

Accepted Answer

A)  $108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }$ 
B)  $108 a ^ { 3 } b ^ { 4 } + 120 a ^ { 2 } b ^ { 3 }$ 
C)  $108 a ^ { 2 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }$ 
D)  $108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 2 }$ 
A)  $108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }$ 
B)  $108 a ^ { 3 } b ^ { 4 } + 120 a ^ { 2 } b ^ { 3 }$ 
C)  $108 a ^ { 2 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }$ 
D)  $108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 2 }$

Question 3

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 3 y ^ { 2 n } + 5 y ^ { n } + 4 \right) + \left( 5 y ^ { 2 n } + 5 y ^ { n } + 8 \right)$$

Accepted Answer

A)  $8 y ^ { 4 n } + 10 y ^ { 2 n } + 12$ 
B)  $9 y ^ { 2 n } + 8 y ^ { n } + 13$ 
C)  $30 y ^ { 3 n }$ 
D)  $8 y ^ { 2 n } + 10 y ^ { n } + 12$ 
A)  $8 y ^ { 4 n } + 10 y ^ { 2 n } + 12$ 
B)  $9 y ^ { 2 n } + 8 y ^ { n } + 13$ 
C)  $30 y ^ { 3 n }$ 
D)  $8 y ^ { 2 n } + 10 y ^ { n } + 12$

Question 4

Find the indicated function value.
-Find $f ( 4 )$ when $f ( x ) = x ^ { 2 } - 5 x - 7$

Accepted Answer

A)  3 
B)  43 
C)  $- 11$ 
D)  29 
A)  3 
B)  43 
C)  $- 11$ 
D)  29

Question 5

Solve the problem.
-A rocket is stopped 28 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 10 feet per second per second. The distance between the rocket and the satellite is given by the polynomial $\mathrm { P } ( \mathrm { t } ) = 5 \mathrm { t } ^ { 2 } + 28$. Find the distance between the rocket and the satellite 9 seconds after the rocket started moving.

Accepted Answer

A)  $109 \mathrm { ft }$ 
B)  $73 \mathrm { ft }$ 
C)  $405 \mathrm { ft }$ 
D)  $433 \mathrm { ft }$ 
A)  $109 \mathrm { ft }$ 
B)  $73 \mathrm { ft }$ 
C)  $405 \mathrm { ft }$ 
D)  $433 \mathrm { ft }$

Question 6

Subtract the polynomials. Assume all variable exponents represent whole numbers.
-Subtract $9 x ^ { 3 } + 11 x ^ { 2 } y + 8 x y ^ { 2 } + 10 y ^ { 3 }$ from $2 x ^ { 3 } + 3 x y ^ { 2 } + 12 y ^ { 3 }$

Accepted Answer

A)  $7 x ^ { 3 } + 11 x ^ { 2 } y + 5 x y ^ { 2 } - 2 y ^ { 3 }$ 
B)  $- 7 x ^ { 3 } - 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }$ 
C)  $11 x ^ { 3 } + 11 x ^ { 2 } y + 10 x y ^ { 2 } + 22 y ^ { 3 }$ 
D)  $- 7 x ^ { 3 } + 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }$ 
A)  $7 x ^ { 3 } + 11 x ^ { 2 } y + 5 x y ^ { 2 } - 2 y ^ { 3 }$ 
B)  $- 7 x ^ { 3 } - 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }$ 
C)  $11 x ^ { 3 } + 11 x ^ { 2 } y + 10 x y ^ { 2 } + 22 y ^ { 3 }$ 
D)  $- 7 x ^ { 3 } + 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }$

Question 7

Solve the problem.
-Write a polynomial that represents the area of the shaded region.

Accepted Answer

A)  $67 x ^ { 2 } - 9$ 
B)  $61 x ^ { 2 } + 9$ 
C)  $64 x ^ { 2 } - 3 x - 9$ 
D)  $61 \mathrm { x } ^ { 2 } - 9$ 
A)  $67 x ^ { 2 } - 9$ 
B)  $61 x ^ { 2 } + 9$ 
C)  $64 x ^ { 2 } - 3 x - 9$ 
D)  $61 \mathrm { x } ^ { 2 } - 9$

Question 8

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 9 \right)$$

Accepted Answer

A)  $x ^ { 4 } + 18 x ^ { 2 } + 81$ 
B)  $x ^ { 4 } - 81$ 
C)  $x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 54 x - 81$ 
D)  $x ^ { 4 } + 6 x ^ { 3 } - 54 x - 81$ 
A)  $x ^ { 4 } + 18 x ^ { 2 } + 81$ 
B)  $x ^ { 4 } - 81$ 
C)  $x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 54 x - 81$ 
D)  $x ^ { 4 } + 6 x ^ { 3 } - 54 x - 81$

Question 9

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$( 3 x - 7 y ) ^ { 2 }$$

Accepted Answer

A)  $9 x ^ { 2 } - 42 x y + 49 y ^ { 2 }$ 
B)  $3 x ^ { 2 } + 49 y ^ { 2 }$ 
C)  $3 x ^ { 2 } - 42 x y + 49 y ^ { 2 }$ 
D)  $9 x ^ { 2 } + 49 y ^ { 2 }$ 
A)  $9 x ^ { 2 } - 42 x y + 49 y ^ { 2 }$ 
B)  $3 x ^ { 2 } + 49 y ^ { 2 }$ 
C)  $3 x ^ { 2 } - 42 x y + 49 y ^ { 2 }$ 
D)  $9 x ^ { 2 } + 49 y ^ { 2 }$

Question 10

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
-$$f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2$$

Accepted Answer

A)  rises to the left and rises to the right
  
B)  falls to the left and falls to the right
  
C)  rises to the left and falls to the right
  
D)  falls to the left and rises to the right
  
A)  rises to the left and rises to the right
  
B)  falls to the left and falls to the right
  
C)  rises to the left and falls to the right
  
D)  falls to the left and rises to the right

Question 11

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$( 5 x + y ) ^ { 2 }$

Accepted Answer

A)  $25 x ^ { 2 } + 10 x y + y ^ { 2 }$ 
B)  $25 x ^ { 2 } + 5 x y + y ^ { 2 }$ 
C)  $25 x ^ { 2 } + 10 x y + 2 y ^ { 2 }$ 
D)  $5 x ^ { 2 } + 10 x y + y ^ { 2 }$ 
A)  $25 x ^ { 2 } + 10 x y + y ^ { 2 }$ 
B)  $25 x ^ { 2 } + 5 x y + y ^ { 2 }$ 
C)  $25 x ^ { 2 } + 10 x y + 2 y ^ { 2 }$ 
D)  $5 x ^ { 2 } + 10 x y + y ^ { 2 }$

Question 12

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$\left( 8 a ^ { n } - 13 b ^ { n } \right) \left( 8 a ^ { n } + 13 b ^ { n } \right)$$

Accepted Answer

A)  $8 a ^ { 2 n } - 13 b ^ { 2 n }$ 
B)  $64 a ^ { 2 n } + 208 a ^ { n } b ^ { n } - 169 b ^ { 2 n }$ 
C)  $64 a ^ { n } - 169 b ^ { n }$ 
D)  $64 \mathrm { a } ^ { 2 \mathrm { n } } - 169 \mathrm {~b} ^ { 2 \mathrm { n } }$ 
A)  $8 a ^ { 2 n } - 13 b ^ { 2 n }$ 
B)  $64 a ^ { 2 n } + 208 a ^ { n } b ^ { n } - 169 b ^ { 2 n }$ 
C)  $64 a ^ { n } - 169 b ^ { n }$ 
D)  $64 \mathrm { a } ^ { 2 \mathrm { n } } - 169 \mathrm {~b} ^ { 2 \mathrm { n } }$

Question 13

Find the product. Assume all variable exponents represent whole numbers.
-$$( p - q ) \left( p ^ { 2 } + p q + q ^ { 2 } \right)$$

Accepted Answer

A)  $p ^ { 3 } - q ^ { 3 }$ 
B)  $p ^ { 3 } - 2 p ^ { 2 } q - 2 p q ^ { 2 } - q ^ { 3 }$ 
C)  $p ^ { 3 } + 2 p ^ { 2 } q + 2 p q ^ { 2 } - q ^ { 3 }$ 
D)  $\mathrm { p } ^ { 3 } + \mathrm { q } ^ { 3 }$ 
A)  $p ^ { 3 } - q ^ { 3 }$ 
B)  $p ^ { 3 } - 2 p ^ { 2 } q - 2 p q ^ { 2 } - q ^ { 3 }$ 
C)  $p ^ { 3 } + 2 p ^ { 2 } q + 2 p q ^ { 2 } - q ^ { 3 }$ 
D)  $\mathrm { p } ^ { 3 } + \mathrm { q } ^ { 3 }$

Question 14

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$$36 x ^ { 5 } y + 28 x y ^ { 4 }$$

Accepted Answer

A)  $4 y \left( 9 x ^ { 5 } + 7 x y ^ { 3 } \right)$ 
B)  $4 x \left( 9 x ^ { 4 } y + 7 y ^ { 4 } \right)$ 
C)  $x y \left( 36 x ^ { 4 } + 28 y ^ { 3 } \right)$ 
D)  $4 x y \left( 9 x ^ { 4 } + 7 y ^ { 3 } \right)$ 
A)  $4 y \left( 9 x ^ { 5 } + 7 x y ^ { 3 } \right)$ 
B)  $4 x \left( 9 x ^ { 4 } y + 7 y ^ { 4 } \right)$ 
C)  $x y \left( 36 x ^ { 4 } + 28 y ^ { 3 } \right)$ 
D)  $4 x y \left( 9 x ^ { 4 } + 7 y ^ { 3 } \right)$

Question 15

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$$y ^ { 2 } + 4 y$$

Accepted Answer

A)  $y ^ { 2 } ( 1 + 4 y )$ 
B)  $y ( y + 4 )$ 
C)  $4 y ( y + 1 )$ 
D)  $4 \left( y ^ { 2 } + y \right)$ 
A)  $y ^ { 2 } ( 1 + 4 y )$ 
B)  $y ( y + 4 )$ 
C)  $4 y ( y + 1 )$ 
D)  $4 \left( y ^ { 2 } + y \right)$

Question 16

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$( 2 x + 11 y ) ( 2 x - 11 y )$$

Accepted Answer

A)  $2 x ^ { 2 } - 11 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 44 x y - 121 y ^ { 2 }$ 
C)  $4 x ^ { 2 } - 44 x y - 121 y ^ { 2 }$ 
D)  $4 x ^ { 2 } - 121 y ^ { 2 }$ 
A)  $2 x ^ { 2 } - 11 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 44 x y - 121 y ^ { 2 }$ 
C)  $4 x ^ { 2 } - 44 x y - 121 y ^ { 2 }$ 
D)  $4 x ^ { 2 } - 121 y ^ { 2 }$

Question 17

Find the product. Assume all variable exponents represent whole numbers.
-$$( x - 11 ) \left( x ^ { 2 } + 2 x - 8 \right)$$

Accepted Answer

A)  $x ^ { 3 } - 9 x ^ { 2 } - 30 x + 88$ 
B)  $x ^ { 3 } + 13 x ^ { 2 } + 30 x + 88$ 
C)  $x ^ { 3 } + 13 x ^ { 2 } + 14 x - 88$ 
D)  $x ^ { 3 } - 9 x ^ { 2 } - 14 x - 88$ 
A)  $x ^ { 3 } - 9 x ^ { 2 } - 30 x + 88$ 
B)  $x ^ { 3 } + 13 x ^ { 2 } + 30 x + 88$ 
C)  $x ^ { 3 } + 13 x ^ { 2 } + 14 x - 88$ 
D)  $x ^ { 3 } - 9 x ^ { 2 } - 14 x - 88$

Question 18

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$\left( 1 + x ^ { 3 } \right) \left( 1 - x ^ { 3 } \right)$$

Accepted Answer

A)  $2 - x ^ { 6 }$ 
B)  $2 - x ^ { 9 }$ 
C)  $1 - x ^ { 6 }$ 
D)  $1 - x ^ { 9 }$ 
A)  $2 - x ^ { 6 }$ 
B)  $2 - x ^ { 9 }$ 
C)  $1 - x ^ { 6 }$ 
D)  $1 - x ^ { 9 }$

Question 19

Solve the problem.
-Write a polynomial that represents the volume of the open box.

Accepted Answer

A)  $45 x + 154 x ^ { 2 } + 121 x ^ { 3 }$ 
B)  $45 x - 154 x ^ { 2 } + 11 x ^ { 3 }$ 
C)  $45 - 154 x + 121 x ^ { 2 }$ 
D)  $45 x - 154 x ^ { 2 } + 121 x ^ { 3 }$ 
A)  $45 x + 154 x ^ { 2 } + 121 x ^ { 3 }$ 
B)  $45 x - 154 x ^ { 2 } + 11 x ^ { 3 }$ 
C)  $45 - 154 x + 121 x ^ { 2 }$ 
D)  $45 x - 154 x ^ { 2 } + 121 x ^ { 3 }$

Question 20

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
-$$( 3 x y + 5 ) ( 4 x y + 9 )$$

Accepted Answer

A)  $12 x ^ { 2 } y ^ { 2 } + 47 x y + 14$ 
B)  $12 x ^ { 2 } y ^ { 2 } + 27 x y + 45$ 
C)  $12 x ^ { 2 } y ^ { 2 } + 47 x y + 45$ 
D)  $7 x ^ { 2 } y ^ { 2 } + 47 x y + 45$ 
A)  $12 x ^ { 2 } y ^ { 2 } + 47 x y + 14$ 
B)  $12 x ^ { 2 } y ^ { 2 } + 27 x y + 45$ 
C)  $12 x ^ { 2 } y ^ { 2 } + 47 x y + 45$ 
D)  $7 x ^ { 2 } y ^ { 2 } + 47 x y + 45$

Find the indicated function value. -Find $f ( 2 )$ when $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x$ .

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers. - $12 a b ^ { 2 } \left( 9 a ^ { 2 } b ^ { 3 } + 10 a b \right)$

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( 3 y ^ { 2 n } + 5 y ^ { n } + 4 \right) + \left( 5 y ^ { 2 n } + 5 y ^ { n } + 8 \right)$

Find the indicated function value. -Find $f ( 4 )$ when $f ( x ) = x ^ { 2 } - 5 x - 7$

Subtract the polynomials. Assume all variable exponents represent whole numbers. -Subtract $9 x ^ { 3 } + 11 x ^ { 2 } y + 8 x y ^ { 2 } + 10 y ^ { 3 }$ from $2 x ^ { 3 } + 3 x y ^ { 2 } + 12 y ^ { 3 }$

Solve the problem. -Write a polynomial that represents the area of the shaded region.

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 9 \right)$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $( 3 x - 7 y ) ^ { 2 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - $f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $( 5 x + y ) ^ { 2 }$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $\left( 8 a ^ { n } - 13 b ^ { n } \right) \left( 8 a ^ { n } + 13 b ^ { n } \right)$

Find the product. Assume all variable exponents represent whole numbers. - $( p - q ) \left( p ^ { 2 } + p q + q ^ { 2 } \right)$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $36 x ^ { 5 } y + 28 x y ^ { 4 }$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $y ^ { 2 } + 4 y$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $( 2 x + 11 y ) ( 2 x - 11 y )$

Find the product. Assume all variable exponents represent whole numbers. - $( x - 11 ) \left( x ^ { 2 } + 2 x - 8 \right)$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $\left( 1 + x ^ { 3 } \right) \left( 1 - x ^ { 3 } \right)$

Solve the problem. -Write a polynomial that represents the volume of the open box.

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - $( 3 x y + 5 ) ( 4 x y + 9 )$

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Exam 5: Polynomials, Polynomial Functions, and Factoring

Find the indicated function value. -Find f(2)f ( 2 )f(2) when f(x)=x3+4x2+9xf ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 xf(x)=x3+4x2+9x .

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers. - 12ab2(9a2b3+10ab)12 a b ^ { 2 } \left( 9 a ^ { 2 } b ^ { 3 } + 10 a b \right)12ab2(9a2b3+10ab)

Add the polynomials. Assume all variable exponents represent whole numbers. - (3y2n+5yn+4)+(5y2n+5yn+8)\left( 3 y ^ { 2 n } + 5 y ^ { n } + 4 \right) + \left( 5 y ^ { 2 n } + 5 y ^ { n } + 8 \right)(3y2n+5yn+4)+(5y2n+5yn+8)

Find the indicated function value. -Find f(4)f ( 4 )f(4) when f(x)=x2−5x−7f ( x ) = x ^ { 2 } - 5 x - 7f(x)=x2−5x−7

Subtract the polynomials. Assume all variable exponents represent whole numbers. -Subtract 9x3+11x2y+8xy2+10y39 x ^ { 3 } + 11 x ^ { 2 } y + 8 x y ^ { 2 } + 10 y ^ { 3 }9x3+11x2y+8xy2+10y3 from 2x3+3xy2+12y32 x ^ { 3 } + 3 x y ^ { 2 } + 12 y ^ { 3 }2x3+3xy2+12y3

Solve the problem. -Write a polynomial that represents the area of the shaded region.

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (x−3)(x+3)(x2+9)( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 9 \right)(x−3)(x+3)(x2+9)

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (3x−7y)2( 3 x - 7 y ) ^ { 2 }(3x−7y)2

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f(x)=6x3−3x2−3x−2f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2f(x)=6x3−3x2−3x−2

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (5x+y)2( 5 x + y ) ^ { 2 }(5x+y)2

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (8an−13bn)(8an+13bn)\left( 8 a ^ { n } - 13 b ^ { n } \right) \left( 8 a ^ { n } + 13 b ^ { n } \right)(8an−13bn)(8an+13bn)

Find the product. Assume all variable exponents represent whole numbers. - (p−q)(p2+pq+q2)( p - q ) \left( p ^ { 2 } + p q + q ^ { 2 } \right)(p−q)(p2+pq+q2)

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 36x5y+28xy436 x ^ { 5 } y + 28 x y ^ { 4 }36x5y+28xy4

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - y2+4yy ^ { 2 } + 4 yy2+4y

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (2x+11y)(2x−11y)( 2 x + 11 y ) ( 2 x - 11 y )(2x+11y)(2x−11y)

Find the product. Assume all variable exponents represent whole numbers. - (x−11)(x2+2x−8)( x - 11 ) \left( x ^ { 2 } + 2 x - 8 \right)(x−11)(x2+2x−8)

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (1+x3)(1−x3)\left( 1 + x ^ { 3 } \right) \left( 1 - x ^ { 3 } \right)(1+x3)(1−x3)