Question 1

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-9

Accepted Answer

A)  monomial of degree 1 
B)  monomial of degree 0 
C)  binomial of degree 0 
D)  binomial of degree 1 
A)  monomial of degree 1 
B)  monomial of degree 0 
C)  binomial of degree 0 
D)  binomial of degree 1

Question 2

Factor.
-$$81 x ^ { 2 } - 18 x + 1$$

Accepted Answer

A)  $( x - 9 ) ^ { 2 }$ 
B)  $( 9 x + 1 ) ( 9 x - 1 )$ 
C)  $( 9 x - 1 ) ^ { 2 }$ 
D)  Prime 
A)  $( x - 9 ) ^ { 2 }$ 
B)  $( 9 x + 1 ) ( 9 x - 1 )$ 
C)  $( 9 x - 1 ) ^ { 2 }$ 
D)  Prime

Question 3

Divide.
-$$\frac { x ^ { 4 } + 16 } { x - 2 }$$

Accepted Answer

A)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 32 } { x - 2 }$ 
B)  $x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8 + \frac { 32 } { x - 2 }$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 16 } { x - 2 }$ 
A)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 32 } { x - 2 }$ 
B)  $x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8 + \frac { 32 } { x - 2 }$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 16 } { x - 2 }$

Question 4

Use synthetic division to divide.
-$$\frac { 5 x ^ { 3 } + 25 x ^ { 2 } + 23 x + 12 } { x + 4 }$$

Accepted Answer

A)  $5 x ^ { 2 } + 5 x + 3$ 
B)  $5 x + 5$ 
C)  $- 5 x ^ { 2 } - 4 x + 3$ 
D)  $\frac { 5 } { 4 } x ^ { 2 } + \frac { 25 } { 4 } x + \frac { 23 } { 4 }$ 
A)  $5 x ^ { 2 } + 5 x + 3$ 
B)  $5 x + 5$ 
C)  $- 5 x ^ { 2 } - 4 x + 3$ 
D)  $\frac { 5 } { 4 } x ^ { 2 } + \frac { 25 } { 4 } x + \frac { 23 } { 4 }$

Question 5

Use substitution to factor the polynomial completely.
-$3 ( a - 4 ) ^ { 2 } + 14 ( a - 4 ) + 15$

Accepted Answer

A)  $( 3 a + 7 ) ( a - 1 )$ 
B)  $( 3 a - 7 ) ( a - 1 )$ 
C)  $( 3 a + 7 ) ( a + 1 )$ 
D)  $( 3 a - 7 ) ( a + 1 )$ 
A)  $( 3 a + 7 ) ( a - 1 )$ 
B)  $( 3 a - 7 ) ( a - 1 )$ 
C)  $( 3 a + 7 ) ( a + 1 )$ 
D)  $( 3 a - 7 ) ( a + 1 )$

Question 6

Multiply.
-$$\begin{array} { r } 
6 x ^ { 2 } + 9 x + 5 \
\times \quad x + 7 \
\hline
\end{array}$$

Accepted Answer

A)  $6 x ^ { 3 } + 51 x ^ { 2 } + 68 x + 35$ 
B)  $48 x ^ { 3 } + 42 x ^ { 2 } + 63 x + 12$ 
C)  $6 x ^ { 3 } + 42 x ^ { 2 } + 63 x + 35$ 
D)  $48 x ^ { 3 } + 72 x ^ { 2 } + 40 x$ 
A)  $6 x ^ { 3 } + 51 x ^ { 2 } + 68 x + 35$ 
B)  $48 x ^ { 3 } + 42 x ^ { 2 } + 63 x + 12$ 
C)  $6 x ^ { 3 } + 42 x ^ { 2 } + 63 x + 35$ 
D)  $48 x ^ { 3 } + 72 x ^ { 2 } + 40 x$

Question 7

Multiply.
-$$( x - 5 y ) ( x - 4 y )$$

Accepted Answer

A)  $x ^ { 2 } - 9 x y - 9 y ^ { 2 }$ 
B)  $x ^ { 2 } - 12 x y + 20 y ^ { 2 }$ 
C)  $x ^ { 2 } - 9 x y + 20 y ^ { 2 }$ 
D)  $x - 9 x y + 20 y$ 
A)  $x ^ { 2 } - 9 x y - 9 y ^ { 2 }$ 
B)  $x ^ { 2 } - 12 x y + 20 y ^ { 2 }$ 
C)  $x ^ { 2 } - 9 x y + 20 y ^ { 2 }$ 
D)  $x - 9 x y + 20 y$

Question 8

Perform the indicated operations and simplify.
-$\left( 6 x ^ { 6 } + 5 x ^ { 3 } \right) + \left( 9 x ^ { 6 } + 6 x ^ { 3 } + 4 \right)$

Accepted Answer

A)  $39 x ^ {10 } $ 
B)  $18 x ^ { 6 } + 12 x ^ { 3 } + 4 x$ 
C)  $4 x + 11 x ^ { 6 } + 13 x ^ { 3 }$ 
D)  $15 x ^ { 6 } + 11 x ^ { 3 } + 4$ 
A)  $39 x ^ {10 } $ 
B)  $18 x ^ { 6 } + 12 x ^ { 3 } + 4 x$ 
C)  $4 x + 11 x ^ { 6 } + 13 x ^ { 3 }$ 
D)  $15 x ^ { 6 } + 11 x ^ { 3 } + 4$

Question 9

Factor the polynomial.
-$$x ^ { 3 } + 8 x ^ { 2 } + x + 8$$

Accepted Answer

A)  $\left( 8 x ^ { 2 } + 8 \right) ( x + 1 )$ 
B)  $\left( x ^ { 2 } + 1 \right) ( 8 x + 8 )$ 
C)  $\left( x ^ { 2 } + 8 \right) ( x + 1 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( x + 8 )$ 
A)  $\left( 8 x ^ { 2 } + 8 \right) ( x + 1 )$ 
B)  $\left( x ^ { 2 } + 1 \right) ( 8 x + 8 )$ 
C)  $\left( x ^ { 2 } + 8 \right) ( x + 1 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( x + 8 )$

Question 10

Solve the equation.
-$$y ^ { 3 } = 64 y$$

Accepted Answer

A)  $\{ 0,64 \}$ 
B)  $\{ - 8,8 \}$ 
C)  $\{ - 8,0,8 \}$ 
D)  $\{ 0,8 \}$ 
A)  $\{ 0,64 \}$ 
B)  $\{ - 8,8 \}$ 
C)  $\{ - 8,0,8 \}$ 
D)  $\{ 0,8 \}$

Question 11

Find the function value.
-If $Q ( x ) = - 4 x ^ { 2 } - 9 x - 2$, find $Q ( - 3 )$

Accepted Answer

A)  $- 65$ 
B)  $- 11$ 
C)  7 
D)  61 
A)  $- 65$ 
B)  $- 11$ 
C)  7 
D)  61

Question 12

Factor the polynomial.
-$$x ^ { 2 } + 39 x + 40$$

Accepted Answer

A)  $( x + 8 ) ( x + 5 )$ 
B)  $( x + 40 ) ( x - 1 )$ 
C)  $( x + 40 ) ( x + 1 )$ 
D)  prime polynomial 
A)  $( x + 8 ) ( x + 5 )$ 
B)  $( x + 40 ) ( x - 1 )$ 
C)  $( x + 40 ) ( x + 1 )$ 
D)  prime polynomial

Question 13

Multiply.
-$$( - 5 x + 6 y ) ( - 4 x - 3 y )$$

Accepted Answer

A)  $20 x ^ { 2 } + 15 x y - 18 y ^ { 2 }$ 
B)  $20 x ^ { 2 } - 24 x y - 18 y ^ { 2 }$ 
C)  $20 x ^ { 2 } - 9 x y - 18 y ^ { 2 }$ 
D)  $20 x ^ { 2 } - 9 x y - 9 y ^ { 2 }$ 
A)  $20 x ^ { 2 } + 15 x y - 18 y ^ { 2 }$ 
B)  $20 x ^ { 2 } - 24 x y - 18 y ^ { 2 }$ 
C)  $20 x ^ { 2 } - 9 x y - 18 y ^ { 2 }$ 
D)  $20 x ^ { 2 } - 9 x y - 9 y ^ { 2 }$

Question 14

Factor completely.
-$$4 x ^ { 2 } + 9$$

Accepted Answer

A)  $( 2 x + 3 ) ^ { 2 }$ 
B)  $( 2 x - 3 ) ^ { 2 }$ 
C)  $( 2 x + 3 ) ( 2 x - 3 )$ 
D)  prime polynomial 
A)  $( 2 x + 3 ) ^ { 2 }$ 
B)  $( 2 x - 3 ) ^ { 2 }$ 
C)  $( 2 x + 3 ) ( 2 x - 3 )$ 
D)  prime polynomial

Question 15

Factor completely.
-$$4 x ^ { 2 } + 20 x + 25 - z ^ { 2 }$$

Accepted Answer

A)  $( 2 x - 5 + z ) ( 2 x - 5 - z )$ 
B)  $( 2 x + 5 + z ) ( 2 x + 5 - z )$ 
C)  $( 2 x - 5 - z ) ^ { 2 }$ 
D)  $( 2 x + 5 - z ) ^ { 2 }$ 
A)  $( 2 x - 5 + z ) ( 2 x - 5 - z )$ 
B)  $( 2 x + 5 + z ) ( 2 x + 5 - z )$ 
C)  $( 2 x - 5 - z ) ^ { 2 }$ 
D)  $( 2 x + 5 - z ) ^ { 2 }$

Question 16

Factor completely.
-$$x ^ { 3 } + y ^ { 6 }$$

Accepted Answer

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

Question 17

Factor.
-$343 y ^ { 3 } - 1$

Accepted Answer

A)  $( 343 y - 1 ) \left( y ^ { 2 } + 7 y + 1 \right)$ 
B)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 7 y + 1 \right)$ 
C)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 1 \right)$ 
D)  $( 7 y + 1 ) \left( 49 y ^ { 2 } - 7 y + 1 \right)$ 
A)  $( 343 y - 1 ) \left( y ^ { 2 } + 7 y + 1 \right)$ 
B)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 7 y + 1 \right)$ 
C)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 1 \right)$ 
D)  $( 7 y + 1 ) \left( 49 y ^ { 2 } - 7 y + 1 \right)$

Question 18

Divide.
-$$\frac { x ^ { 3 } + 343 } { x + 7 }$$

Accepted Answer

A)  $x ^ { 2 } + 49$ 
B)  $x ^ { 2 } + 7 x + 49$ 
C)  $x ^ { 2 } - 7 x + 49$ 
D)  $x ^ { 2 } + 7 x - 49$ 
A)  $x ^ { 2 } + 49$ 
B)  $x ^ { 2 } + 7 x + 49$ 
C)  $x ^ { 2 } - 7 x + 49$ 
D)  $x ^ { 2 } + 7 x - 49$

Question 19

Solve.
-Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Accepted Answer

A)  9 m 
B)  17 m 
C)  10 m 
D)  18 m 
A)  9 m 
B)  17 m 
C)  10 m 
D)  18 m

Question 20

Factor the polynomial.
-$$7 x ^ { 2 } z - 7 x z - 42 z$$

Accepted Answer

A)  $7 \mathrm { z } ( \mathrm { x } + 2 ) ( \mathrm { x } - 3 )$ 
B)  $7 \mathrm { z } ( \mathrm { x } - 2 ) ( \mathrm { x } + 3 )$ 
C)  $7 ( x z + 2 ) ( x z - 3 )$ 
D)  prime polynomial 
A)  $7 \mathrm { z } ( \mathrm { x } + 2 ) ( \mathrm { x } - 3 )$ 
B)  $7 \mathrm { z } ( \mathrm { x } - 2 ) ( \mathrm { x } + 3 )$ 
C)  $7 ( x z + 2 ) ( x z - 3 )$ 
D)  prime polynomial

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. -9

Factor. - $81 x ^ { 2 } - 18 x + 1$

Divide. - $\frac { x ^ { 4 } + 16 } { x - 2 }$

Use synthetic division to divide. - $\frac { 5 x ^ { 3 } + 25 x ^ { 2 } + 23 x + 12 } { x + 4 }$

Use substitution to factor the polynomial completely. - $3 ( a - 4 ) ^ { 2 } + 14 ( a - 4 ) + 15$

Multiply. - 6+9x+5 \timesx+7

Multiply. - $( x - 5 y ) ( x - 4 y )$

Perform the indicated operations and simplify. - $\left( 6 x ^ { 6 } + 5 x ^ { 3 } \right) + \left( 9 x ^ { 6 } + 6 x ^ { 3 } + 4 \right)$

Factor the polynomial. - $x ^ { 3 } + 8 x ^ { 2 } + x + 8$

Solve the equation. - $y ^ { 3 } = 64 y$

Find the function value. -If $Q ( x ) = - 4 x ^ { 2 } - 9 x - 2$ , find $Q ( - 3 )$

Factor the polynomial. - $x ^ { 2 } + 39 x + 40$

Multiply. - $( - 5 x + 6 y ) ( - 4 x - 3 y )$

Factor completely. - $4 x ^ { 2 } + 9$

Factor completely. - $4 x ^ { 2 } + 20 x + 25 - z ^ { 2 }$

Factor completely. - $x ^ { 3 } + y ^ { 6 }$

Factor. - $343 y ^ { 3 } - 1$

Divide. - $\frac { x ^ { 3 } + 343 } { x + 7 }$

Solve. -Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Factor the polynomial. - $7 x ^ { 2 } z - 7 x z - 42 z$

Real Numbers and Algebraic Expressions

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Exam 5: Polynomials and Polynomial Functions

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. -9

Factor. - 81x2−18x+181 x ^ { 2 } - 18 x + 181x2−18x+1

Divide. - x4+16x−2\frac { x ^ { 4 } + 16 } { x - 2 }x−2x4+16​

Use synthetic division to divide. - 5x3+25x2+23x+12x+4\frac { 5 x ^ { 3 } + 25 x ^ { 2 } + 23 x + 12 } { x + 4 }x+45x3+25x2+23x+12​

Use substitution to factor the polynomial completely. - 3(a−4)2+14(a−4)+153 ( a - 4 ) ^ { 2 } + 14 ( a - 4 ) + 153(a−4)2+14(a−4)+15

Multiply. - 6+9x+5 \timesx+7

Multiply. - (x−5y)(x−4y)( x - 5 y ) ( x - 4 y )(x−5y)(x−4y)

Perform the indicated operations and simplify. - (6x6+5x3)+(9x6+6x3+4)\left( 6 x ^ { 6 } + 5 x ^ { 3 } \right) + \left( 9 x ^ { 6 } + 6 x ^ { 3 } + 4 \right)(6x6+5x3)+(9x6+6x3+4)

Factor the polynomial. - x3+8x2+x+8x ^ { 3 } + 8 x ^ { 2 } + x + 8x3+8x2+x+8

Solve the equation. - y3=64yy ^ { 3 } = 64 yy3=64y

Find the function value. -If Q(x)=−4x2−9x−2Q ( x ) = - 4 x ^ { 2 } - 9 x - 2Q(x)=−4x2−9x−2 , find Q(−3)Q ( - 3 )Q(−3)

Factor the polynomial. - x2+39x+40x ^ { 2 } + 39 x + 40x2+39x+40

Multiply. - (−5x+6y)(−4x−3y)( - 5 x + 6 y ) ( - 4 x - 3 y )(−5x+6y)(−4x−3y)

Factor completely. - 4x2+94 x ^ { 2 } + 94x2+9

Factor completely. - 4x2+20x+25−z24 x ^ { 2 } + 20 x + 25 - z ^ { 2 }4x2+20x+25−z2

Factor completely. - x3+y6x ^ { 3 } + y ^ { 6 }x3+y6

Factor. - 343y3−1343 y ^ { 3 } - 1343y3−1

Divide. - x3+343x+7\frac { x ^ { 3 } + 343 } { x + 7 }x+7x3+343​