Question 1

Factor the polynomial.
-$$x ^ { 2 } - x - 45$$

Accepted Answer

A)  $( x - 45 ) ( x + 1 )$ 
B)  $( x - 5 ) ( x + 9 )$ 
C)  $( x + 5 ) ( x - 9 )$ 
D)  prime polynomial 
A)  $( x - 45 ) ( x + 1 )$ 
B)  $( x - 5 ) ( x + 9 )$ 
C)  $( x + 5 ) ( x - 9 )$ 
D)  prime polynomial

Question 2

Find the function value.
-If $P ( x ) = 9 x - 7$, find $P ( - 5 )$.

Accepted Answer

A)  52 
B)  38 
C)  $- 38$ 
D)  $- 52$ 
A)  52 
B)  38 
C)  $- 38$ 
D)  $- 52$

Question 3

Multiply.
-$$( x - 11 ) \left( x ^ { 2 } + 4 x - 8 \right)$$

Accepted Answer

A)  $x ^ { 3 } - 7 x ^ { 2 } - 52 x + 88$ 
B)  $x ^ { 3 } + 15 x ^ { 2 } + 36 x - 88$ 
C)  $x ^ { 3 } + 15 x ^ { 2 } + 52 x + 88$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } - 36 x - 88$ 
A)  $x ^ { 3 } - 7 x ^ { 2 } - 52 x + 88$ 
B)  $x ^ { 3 } + 15 x ^ { 2 } + 36 x - 88$ 
C)  $x ^ { 3 } + 15 x ^ { 2 } + 52 x + 88$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } - 36 x - 88$

Question 4

Solve.
-The volume $V ( x )$ of a box in terms of its height $x$ is given by the function $V ( x ) = 15 x ^ { 3 } + 32 x ^ { 2 } + 16 x$. Factor this expression for $\mathrm { V } ( \mathrm { x } )$.

Accepted Answer

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

Question 5

Solve.
-A window washer accidentally drops a bucket from the top of a 64-foot building. After t seconds, the height h(t) is given by the function h(t) = -16t2 + 64. Find how long it takes the bucket to hit the ground.

Accepted Answer

A)  4 sec 
B)  2 sec 
C)  64 sec 
D)  32 sec 
A)  4 sec 
B)  2 sec 
C)  64 sec 
D)  32 sec

Question 6

Perform the indicated operation.
-$$( 12 \mathrm {~m} - \mathrm { n } ) ^ { 2 }$$

Accepted Answer

A)  $144 m ^ { 2 } - 12 m n + n ^ { 2 }$ 
B)  $144 m ^ { 2 } + n ^ { 2 }$ 
C)  $144 m ^ { 2 } - 24 m n - 2 n ^ { 2 }$ 
D)  $144 m ^ { 2 } - 24 m n + n ^ { 2 }$ 
A)  $144 m ^ { 2 } - 12 m n + n ^ { 2 }$ 
B)  $144 m ^ { 2 } + n ^ { 2 }$ 
C)  $144 m ^ { 2 } - 24 m n - 2 n ^ { 2 }$ 
D)  $144 m ^ { 2 } - 24 m n + n ^ { 2 }$

Question 7

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-$$4 \mathrm { z } ^ { 2 } + \mathrm { z }$$

Accepted Answer

A)  trinomial of degree 2 
B)  binomial of degree 2 
C)  binomial of degree 4 
D)  binomial of degree 1 
A)  trinomial of degree 2 
B)  binomial of degree 2 
C)  binomial of degree 4 
D)  binomial of degree 1

Question 8

Factor.
-$$\frac { 1 } { 16 } - x ^ { 2 }$$

Accepted Answer

A)  $\left( \frac { 1 } { 4 } + x \right) ^ { 2 }$ 
B)  $\left( \frac { 1 } { 4 } - x \right) ^ { 2 }$ 
C)  $\left( \frac { 1 } { 4 } - x \right) \left( \frac { 1 } { 4 } + x \right)$ 
D)  prime polynomial 
A)  $\left( \frac { 1 } { 4 } + x \right) ^ { 2 }$ 
B)  $\left( \frac { 1 } { 4 } - x \right) ^ { 2 }$ 
C)  $\left( \frac { 1 } { 4 } - x \right) \left( \frac { 1 } { 4 } + x \right)$ 
D)  prime polynomial

Question 9

Find the perimeter.
-

Accepted Answer

A)  $\left( x ^ { 2 } + 8 x + 4 \right)$ units 
B)  $\left( x ^ { 4 } + 8 x ^ { 2 } + 4 \right)$ units 
C)  $\left( 4 x ^ { 2 } + 16 x + 8 \right)$ units 
D)  $\left( x ^ { 4 } + 16 x ^ { 2 } + 8 \right)$ units 
A)  $\left( x ^ { 2 } + 8 x + 4 \right)$ units 
B)  $\left( x ^ { 4 } + 8 x ^ { 2 } + 4 \right)$ units 
C)  $\left( 4 x ^ { 2 } + 16 x + 8 \right)$ units 
D)  $\left( x ^ { 4 } + 16 x ^ { 2 } + 8 \right)$ units

Question 10

Factor.
-$49 x ^ { 2 } - 16 y ^ { 2 }$

Accepted Answer

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

Question 11

Factor the polynomial completely.
-$7 x ^ { 2 } - 21 x z - 28 z ^ { 2 }$

Accepted Answer

A)  $7 ( x - z ) ( x + 4 z )$ 
B)  $7 ( x + z ) ( x - 4 z )$ 
C)  $( 7 x - 7 z ) ( x + 4 z )$ 
D)  prime polynomial 
A)  $7 ( x - z ) ( x + 4 z )$ 
B)  $7 ( x + z ) ( x - 4 z )$ 
C)  $( 7 x - 7 z ) ( x + 4 z )$ 
D)  prime polynomial

Question 12

Factor the polynomial by grouping.
-$$x y - 3 y z + 9 x - 27 z$$

Accepted Answer

A)  $( y + 3 ) ( x - 9 z )$ 
B)  $( y - 9 ) ( x + 3 z )$ 
C)  $( y - 3 ) ( x + 9 z )$ 
D)  $( y + 9 ) ( x - 3 z )$ 
A)  $( y + 3 ) ( x - 9 z )$ 
B)  $( y - 9 ) ( x + 3 z )$ 
C)  $( y - 3 ) ( x + 9 z )$ 
D)  $( y + 9 ) ( x - 3 z )$

Question 13

Solve.
-The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 48 square centimeters. Find the side of the
Square.

Accepted Answer

A)  6 cm 
B)  16 cm 
C)  4 cm 
D)  2 cm 
A)  6 cm 
B)  16 cm 
C)  4 cm 
D)  2 cm

Question 14

Factor. Assume that variables used as exponents represent positive integers.
-$x ^ { 2 n } - 4$

Accepted Answer

A)  $\left( x ^ { n } - 2 \right) ^ { 2 }$ 
B)  $\left( x ^ { n } + 2 \right) \left( x ^ { n } - 2 \right)$ 
C)  $\left( x ^ { n } + 2 \right) ^ { 2 }$ 
D)  prime polynomial 
A)  $\left( x ^ { n } - 2 \right) ^ { 2 }$ 
B)  $\left( x ^ { n } + 2 \right) \left( x ^ { n } - 2 \right)$ 
C)  $\left( x ^ { n } + 2 \right) ^ { 2 }$ 
D)  prime polynomial

Question 15

Divide.
-$21 r ^ { 6 } - 35 r ^ { 3 }$ by $7 r$

Accepted Answer

A)  $3 r ^ { 6 } - 5 r ^ { 3 }$ 
B)  $21 r ^ { 5 } - 35 r ^ { 2 }$ 
C)  $3 r ^ { 5 } - 5 r ^ { 2 }$ 
D)  $3 r ^ { 7 } - 5 r ^ { 4 }$ 
A)  $3 r ^ { 6 } - 5 r ^ { 3 }$ 
B)  $21 r ^ { 5 } - 35 r ^ { 2 }$ 
C)  $3 r ^ { 5 } - 5 r ^ { 2 }$ 
D)  $3 r ^ { 7 } - 5 r ^ { 4 }$

Question 16

Multiply.
-$- 2 x ^ { 2 } y \left( - 3 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 3 } + 10 \right)$

Accepted Answer

A)  $6 x ^ { 4 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20 x ^ { 2 } y$ 
B)  $6 x ^ { 4 } y ^ { 5 } - 12 x ^ { 3 } y ^ { 4 } + 20 x ^ { 2 } y$ 
C)  $6 x ^ { 4 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20$ 
D)  $6 x ^ { 2 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20 x ^ { 2 } y$ 
A)  $6 x ^ { 4 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20 x ^ { 2 } y$ 
B)  $6 x ^ { 4 } y ^ { 5 } - 12 x ^ { 3 } y ^ { 4 } + 20 x ^ { 2 } y$ 
C)  $6 x ^ { 4 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20$ 
D)  $6 x ^ { 2 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20 x ^ { 2 } y$

Question 17

Subtract.
-$$\left( x ^ { 3 } + 9 x y - 4 y ^ { 2 } \right) - \left( 6 x ^ { 3 } + 4 x y + y ^ { 2 } \right)$$

Accepted Answer

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

Question 18

Subtract.
-$$\left( - 9 a ^ { 2 } b ^ { 4 } + 3 a b ^ { 2 } + 4 a b \right) - \left( 7 a ^ { 2 } b ^ { 4 } + 5 a b ^ { 2 } - a b \right)$$

Accepted Answer

A)  $16 a ^ { 2 } b ^ { 4 } + 2 a b ^ { 2 } - 5 a b$ 
B)  $- 16 a ^ { 2 } b ^ { 4 } - 2 a b ^ { 2 } + 5 a b$ 
C)  $- 16 a ^ { 2 } b ^ { 4 } + 2 a b ^ { 2 } + 3 a b$ 
D)  $- 2 a ^ { 2 } b ^ { 4 } + 8 a b ^ { 2 } + 3 a b$ 
A)  $16 a ^ { 2 } b ^ { 4 } + 2 a b ^ { 2 } - 5 a b$ 
B)  $- 16 a ^ { 2 } b ^ { 4 } - 2 a b ^ { 2 } + 5 a b$ 
C)  $- 16 a ^ { 2 } b ^ { 4 } + 2 a b ^ { 2 } + 3 a b$ 
D)  $- 2 a ^ { 2 } b ^ { 4 } + 8 a b ^ { 2 } + 3 a b$

Question 19

Perform the indicated operation.
-$- 8 x y ( 12 x - 2 y )$

Accepted Answer

A)  $96 x ^ { 2 } y + 16 x y ^ { 2 }$ 
B)  $- 96 x ^ { 2 } y - 16 x y ^ { 2 }$ 
C)  $- 96 x ^ { 2 } y + 16 x y ^ { 2 }$ 
D)  $96 x ^ { 2 } y - 16 x y ^ { 2 }$ 
A)  $96 x ^ { 2 } y + 16 x y ^ { 2 }$ 
B)  $- 96 x ^ { 2 } y - 16 x y ^ { 2 }$ 
C)  $- 96 x ^ { 2 } y + 16 x y ^ { 2 }$ 
D)  $96 x ^ { 2 } y - 16 x y ^ { 2 }$

Question 20

Solve.
-A rectangular floor measures 24 feet by 7 feet. Find the length of the diagonal of the floor.

Accepted Answer

A)  312.5 ft 
B)  24 ft 
C)  26 ft 
D)  25 ft 
A)  312.5 ft 
B)  24 ft 
C)  26 ft 
D)  25 ft

Factor the polynomial. - $x ^ { 2 } - x - 45$

Find the function value. -If $P ( x ) = 9 x - 7$ , find $P ( - 5 )$ .

Multiply. - $( x - 11 ) \left( x ^ { 2 } + 4 x - 8 \right)$

Solve. -A window washer accidentally drops a bucket from the top of a 64-foot building. After t seconds, the height h(t) is given by the function h(t) = -16t2 + 64. Find how long it takes the bucket to hit the ground.

Perform the indicated operation. - $( 12 \mathrm {~m} - \mathrm { n } ) ^ { 2 }$

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - $4 \mathrm { z } ^ { 2 } + \mathrm { z }$

Factor. - $\frac { 1 } { 16 } - x ^ { 2 }$

Find the perimeter. -

Factor. - $49 x ^ { 2 } - 16 y ^ { 2 }$

Factor the polynomial completely. - $7 x ^ { 2 } - 21 x z - 28 z ^ { 2 }$

Factor the polynomial by grouping. - $x y - 3 y z + 9 x - 27 z$

Solve. -The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 48 square centimeters. Find the side of the Square.

Factor. Assume that variables used as exponents represent positive integers. - $x ^ { 2 n } - 4$

Divide. - $21 r ^ { 6 } - 35 r ^ { 3 }$ by $7 r$

Multiply. - $- 2 x ^ { 2 } y \left( - 3 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 3 } + 10 \right)$

Subtract. - $\left( x ^ { 3 } + 9 x y - 4 y ^ { 2 } \right) - \left( 6 x ^ { 3 } + 4 x y + y ^ { 2 } \right)$

Subtract. - $\left( - 9 a ^ { 2 } b ^ { 4 } + 3 a b ^ { 2 } + 4 a b \right) - \left( 7 a ^ { 2 } b ^ { 4 } + 5 a b ^ { 2 } - a b \right)$

Perform the indicated operation. - $- 8 x y ( 12 x - 2 y )$

Solve. -A rectangular floor measures 24 feet by 7 feet. Find the length of the diagonal of the floor.

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Exam 5: Polynomials and Polynomial Functions

Factor the polynomial. - x2−x−45x ^ { 2 } - x - 45x2−x−45

Find the function value. -If P(x)=9x−7P ( x ) = 9 x - 7P(x)=9x−7 , find P(−5)P ( - 5 )P(−5) .

Multiply. - (x−11)(x2+4x−8)( x - 11 ) \left( x ^ { 2 } + 4 x - 8 \right)(x−11)(x2+4x−8)

Solve. -The volume V(x)V ( x )V(x) of a box in terms of its height xxx is given by the function V(x)=15x3+32x2+16xV ( x ) = 15 x ^ { 3 } + 32 x ^ { 2 } + 16 xV(x)=15x3+32x2+16x . Factor this expression for V(x)\mathrm { V } ( \mathrm { x } )V(x) .