Question 1

Divide.
-$$\left( x ^ { 2 } + 15 x + 50 \right) \div ( x + 5 )$$

Accepted Answer

A)  $x + 15$ 
B)  $x ^ { 2 } + 15$ 
C)  $x + 10$ 
D)  $x ^ { 2 } + 10$ 
A)  $x + 15$ 
B)  $x ^ { 2 } + 15$ 
C)  $x + 10$ 
D)  $x ^ { 2 } + 10$

Question 2

Fill in the blank with one of the words or phrases listed below.

-A is a polynomial with two terms.

Accepted Answer

A)  binomial 
B)  quadratic equation 
C)  trinomial 
D)  monomial 
A)  binomial 
B)  quadratic equation 
C)  trinomial 
D)  monomial

Question 3

Use substitution to factor the polynomial completely.
-$15 x ^ { 4 } + 19 x ^ { 2 } + 6$

Accepted Answer

A)  $\left( 5 x ^ { 2 } - 3 \right) \left( 3 x ^ { 2 } - 2 \right)$ 
B)  $\left( 15 x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 3 \right)$ 
C)  $\left( 3 x ^ { 2 } + 2 \right) \left( 5 x ^ { 2 } + 3 \right)$ 
D)  $\left( 3 x ^ { 2 } + 1 \right) \left( 5 x ^ { 2 } + 6 \right)$ 
A)  $\left( 5 x ^ { 2 } - 3 \right) \left( 3 x ^ { 2 } - 2 \right)$ 
B)  $\left( 15 x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 3 \right)$ 
C)  $\left( 3 x ^ { 2 } + 2 \right) \left( 5 x ^ { 2 } + 3 \right)$ 
D)  $\left( 3 x ^ { 2 } + 1 \right) \left( 5 x ^ { 2 } + 6 \right)$

Question 4

Factor the polynomial.
-$$x ^ { 2 } + 9 x + 14$$

Accepted Answer

A)  $( x - 7 ) ( x + 2 )$ 
B)  $( x - 7 ) ( x + 1 )$ 
C)  $( x + 7 ) ( x + 2 )$ 
D)  prime polynomial 
A)  $( x - 7 ) ( x + 2 )$ 
B)  $( x - 7 ) ( x + 1 )$ 
C)  $( x + 7 ) ( x + 2 )$ 
D)  prime polynomial

Question 5

Match the polynomial function with its graph.
-$$f ( x ) = x ( x - 1 ) ( x + 1 )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Factor the polynomial completely.
-$x ^ { 5 } - 7 x ^ { 4 } - 18 x ^ { 3 }$

Accepted Answer

A)  $x ^ { 3 } ( x - 9 ) ( x - 2 )$ 
B)  $x ^ { 3 } \left( x ^ { 2 } - 7 x - 18 \right)$ 
C)  $x ^ { 3 } ( x - 9 ) ( x + 2 )$ 
D)  $x ^ { 3 } ( x + 9 ) ( x + 2 )$ 
A)  $x ^ { 3 } ( x - 9 ) ( x - 2 )$ 
B)  $x ^ { 3 } \left( x ^ { 2 } - 7 x - 18 \right)$ 
C)  $x ^ { 3 } ( x - 9 ) ( x + 2 )$ 
D)  $x ^ { 3 } ( x + 9 ) ( x + 2 )$

Question 7

Multiply.
-$$( x - 4 ) ^ { 2 }$$

Accepted Answer

A)  $x ^ { 2 } - 8 x + 16$ 
B)  $x + 16$ 
C)  $x ^ { 2 } + 16$ 
D)  $16 x ^ { 2 } - 8 x + 16$ 
A)  $x ^ { 2 } - 8 x + 16$ 
B)  $x + 16$ 
C)  $x ^ { 2 } + 16$ 
D)  $16 x ^ { 2 } - 8 x + 16$

Question 8

Divide.
-$$\left( 2 x ^ { 5 } - x ^ { 3 } - 4 x ^ { 2 } - 12 x + 12 \right) \div \left( x ^ { 2 } - 3 \right)$$

Accepted Answer

A)  $2 x ^ { 3 } + 5 x - 4 + \frac { 3 x + 24 } { x ^ { 2 } - 3 }$ 
B)  $2 x ^ { 3 } + 5 x + 4 + \frac { 3 x } { x ^ { 2 } - 3 }$ 
C)  $2 x ^ { 3 } + 5 x - 4 + \frac { 3 x } { x ^ { 2 } - 3 }$ 
D)  $2 x ^ { 3 } + 5 x - 4 - \frac { 3 x } { x ^ { 2 } - 3 }$ 
A)  $2 x ^ { 3 } + 5 x - 4 + \frac { 3 x + 24 } { x ^ { 2 } - 3 }$ 
B)  $2 x ^ { 3 } + 5 x + 4 + \frac { 3 x } { x ^ { 2 } - 3 }$ 
C)  $2 x ^ { 3 } + 5 x - 4 + \frac { 3 x } { x ^ { 2 } - 3 }$ 
D)  $2 x ^ { 3 } + 5 x - 4 - \frac { 3 x } { x ^ { 2 } - 3 }$

Question 9

Fill in the blank with one of the words or phrases listed below.

-If a and b are real numbers and a · b = , then a = 0 or b = 0.

Accepted Answer

A)  quadratic equation 
B)  0 
C)  degree of a term 
D)  degree of a polynomial 
A)  quadratic equation 
B)  0 
C)  degree of a term 
D)  degree of a polynomial

Question 10

Multiply. Assume that variables used as exponents represent positive integers.
-$$9 x ^ { 2 } y ^ { n } \left( - 3 x y ^ { n } + 1 + 2 \right)$$

Accepted Answer

A)  $- 27 x ^ { 3 } y ^ { n ^ { 2 } + 1 } + 18 x ^ { 2 } y ^ { n }$ 
B)  $- 27 x ^ { 3 } y ^ { 2 n } + 18 x ^ { 2 } y ^ { n }$ 
C)  $- 27 x ^ { 2 } y ^ { 2 n } + 1 + 18 x ^ { 2 } y ^ { n }$ 
D)  $- 27 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 2 \mathrm { n } + 1 } + 18 \mathrm { x } ^ { 2 } \mathrm { y } \mathrm { n }$ 
A)  $- 27 x ^ { 3 } y ^ { n ^ { 2 } + 1 } + 18 x ^ { 2 } y ^ { n }$ 
B)  $- 27 x ^ { 3 } y ^ { 2 n } + 18 x ^ { 2 } y ^ { n }$ 
C)  $- 27 x ^ { 2 } y ^ { 2 n } + 1 + 18 x ^ { 2 } y ^ { n }$ 
D)  $- 27 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 2 \mathrm { n } + 1 } + 18 \mathrm { x } ^ { 2 } \mathrm { y } \mathrm { n }$

Question 11

Solve the equation.
-$$x ^ { 6 } = 9 x ^ { 4 }$$

Accepted Answer

A)  $\{ - 3,3 \}$ 
B)  $\{ 0,3 \}$ 
C)  $\{ - 3,0,3 \}$ 
D)  $\{ 0,9 \}$ 
A)  $\{ - 3,3 \}$ 
B)  $\{ 0,3 \}$ 
C)  $\{ - 3,0,3 \}$ 
D)  $\{ 0,9 \}$

Question 12

Factor the trinomial.
-$25 y ^ { 3 } + 40 y ^ { 2 } + 16 y$

Accepted Answer

A)  $y ( 5 y - 4 ) ^ { 2 }$ 
B)  $y ( 25 y + 1 ) ( y + 16 )$ 
C)  $y ( 5 y + 4 ) ( 5 y - 4 )$ 
D)  $y ( 5 y + 4 ) ^ { 2 }$ 
A)  $y ( 5 y - 4 ) ^ { 2 }$ 
B)  $y ( 25 y + 1 ) ( y + 16 )$ 
C)  $y ( 5 y + 4 ) ( 5 y - 4 )$ 
D)  $y ( 5 y + 4 ) ^ { 2 }$

Question 13

Find the function value.
-If $P ( x ) = x ^ { 2 } + 7 x - 4$, find $P ( 4 )$

Accepted Answer

A)  40 
B)  28 
C)  19 
D)  44 
A)  40 
B)  28 
C)  19 
D)  44

Question 14

Multiply.
-$\left( 5.8 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 2 } \mathrm { z } \right) \left( 10 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 5 } \mathrm { z } ^ { 9 } \right)$

Accepted Answer

A)  $58 x ^ { 8 } y ^ { 7 } z ^ { 10 }$ 
B)  $580 \mathrm { x } 1 \mathrm { y } _ { \mathrm { y } } 10 _ { \mathrm { z } } \mathrm { 9 }$ 
C)  $58 \mathrm { x } ^ { 15 } \mathrm { y } ^ { 10 } \mathrm { z } 9$ 
D)  $5.8 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 7 } \mathrm { z } ^ { 10 }$ 
A)  $58 x ^ { 8 } y ^ { 7 } z ^ { 10 }$ 
B)  $580 \mathrm { x } 1 \mathrm { y } _ { \mathrm { y } } 10 _ { \mathrm { z } } \mathrm { 9 }$ 
C)  $58 \mathrm { x } ^ { 15 } \mathrm { y } ^ { 10 } \mathrm { z } 9$ 
D)  $5.8 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 7 } \mathrm { z } ^ { 10 }$

Question 15

Multiply.
-$\left( 5 x y ^ { 2 } + 12 x \right) \left( 5 x y ^ { 2 } - 12 x \right)$

Accepted Answer

A)  $10 x ^ { 2 } y ^ { 4 } - 120 x ^ { 2 } y ^ { 2 } - 24 x ^ { 2 }$ 
B)  $10 x ^ { 2 } y ^ { 4 } - 24 x ^ { 2 }$ 
C)  $25 x ^ { 2 } y ^ { 4 } - 120 x ^ { 2 } y ^ { 2 } - 144 x ^ { 2 }$ 
D)  $25 x ^ { 2 } y ^ { 4 } - 144 x ^ { 2 }$ 
A)  $10 x ^ { 2 } y ^ { 4 } - 120 x ^ { 2 } y ^ { 2 } - 24 x ^ { 2 }$ 
B)  $10 x ^ { 2 } y ^ { 4 } - 24 x ^ { 2 }$ 
C)  $25 x ^ { 2 } y ^ { 4 } - 120 x ^ { 2 } y ^ { 2 } - 144 x ^ { 2 }$ 
D)  $25 x ^ { 2 } y ^ { 4 } - 144 x ^ { 2 }$

Question 16

Factor the trinomial.
-$$6 x ^ { 2 } - 26 x - 20$$

Accepted Answer

A)  $( 6 x + 4 ) ( x - 5 )$ 
B)  $2 ( 3 x + 2 ) ( x - 5 )$ 
C)  $2 ( 3 x - 2 ) ( x + 5 )$ 
D)  prime polynomial 
A)  $( 6 x + 4 ) ( x - 5 )$ 
B)  $2 ( 3 x + 2 ) ( x - 5 )$ 
C)  $2 ( 3 x - 2 ) ( x + 5 )$ 
D)  prime polynomial

Question 17

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

Accepted Answer

A)  $x ^ { 3 } - 9 x + 18$ 
B)  $x ^ { 3 } - 6 x ^ { 2 } - 3 x + 18$ 
C)  $x ^ { 3 } - 9 x ^ { 2 } + 18$ 
D)  $x ^ { 3 } + 6 x ^ { 2 } + 3 x + 18$ 
A)  $x ^ { 3 } - 9 x + 18$ 
B)  $x ^ { 3 } - 6 x ^ { 2 } - 3 x + 18$ 
C)  $x ^ { 3 } - 9 x ^ { 2 } + 18$ 
D)  $x ^ { 3 } + 6 x ^ { 2 } + 3 x + 18$

Question 18

For the given f(x $$f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$$
-$$f ( x ) = x ^ { 2 } + 8 x + 7 ; g ( x ) = x + 2$$

Accepted Answer

A)  $x + 6 - \frac { 5 } { x + 2 } ; x \neq 2$ 
B)  $x + 6 + \frac { 5 } { x + 2 } ; x \neq - 2$ 
C)  $x + 6 - \frac { 5 } { x + 2 } ; x \neq - 2$ 
D)  $x + 6 - \frac { 5 } { x + 2 } ; x \neq 0$ 
A)  $x + 6 - \frac { 5 } { x + 2 } ; x \neq 2$ 
B)  $x + 6 + \frac { 5 } { x + 2 } ; x \neq - 2$ 
C)  $x + 6 - \frac { 5 } { x + 2 } ; x \neq - 2$ 
D)  $x + 6 - \frac { 5 } { x + 2 } ; x \neq 0$

Question 19

Simplify the polynomial by combining like terms.
-$$\left( 5 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 6 x y \right) + \left( 3 x ^ { 5 } y ^ { 3 } + 11 x ^ { 3 } y + 12 x y \right)$$

Accepted Answer

A)  $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y ^ { 2 } + 18 x y$ 
B)  $8 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 11 x ^ { 3 } y + 18 x y$ 
C)  $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y + 18 x y$ 
D)  $21 x ^ { 6 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } + 18 x y$ 
A)  $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y ^ { 2 } + 18 x y$ 
B)  $8 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 11 x ^ { 3 } y + 18 x y$ 
C)  $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y + 18 x y$ 
D)  $21 x ^ { 6 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } + 18 x y$

Question 20

Find the function.
-If $P ( x ) = x - 6$ and $Q ( x ) = x ^ { 2 } - 11$, find $P ( x ) \cdot Q ( x )$.

Accepted Answer

A)  $x ^ { 3 } - 6 x ^ { 2 } - 17 x + 66$ 
B)  $x ^ { 3 } - 17 x ^ { 2 } + 66$ 
C)  $x ^ { 2 } - 17 x + 66$ 
D)  $x ^ { 3 } - 6 x ^ { 2 } - 11 x + 66$ 
A)  $x ^ { 3 } - 6 x ^ { 2 } - 17 x + 66$ 
B)  $x ^ { 3 } - 17 x ^ { 2 } + 66$ 
C)  $x ^ { 2 } - 17 x + 66$ 
D)  $x ^ { 3 } - 6 x ^ { 2 } - 11 x + 66$

Divide. - $\left( x ^ { 2 } + 15 x + 50 \right) \div ( x + 5 )$

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with two terms.

Use substitution to factor the polynomial completely. - $15 x ^ { 4 } + 19 x ^ { 2 } + 6$

Factor the polynomial. - $x ^ { 2 } + 9 x + 14$

Match the polynomial function with its graph. - $f ( x ) = x ( x - 1 ) ( x + 1 )$

Factor the polynomial completely. - $x ^ { 5 } - 7 x ^ { 4 } - 18 x ^ { 3 }$

Multiply. - $( x - 4 ) ^ { 2 }$

Divide. - $\left( 2 x ^ { 5 } - x ^ { 3 } - 4 x ^ { 2 } - 12 x + 12 \right) \div \left( x ^ { 2 } - 3 \right)$

Fill in the blank with one of the words or phrases listed below. -If a and b are real numbers and a · b = , then a = 0 or b = 0.

Multiply. Assume that variables used as exponents represent positive integers. - $9 x ^ { 2 } y ^ { n } \left( - 3 x y ^ { n } + 1 + 2 \right)$

Solve the equation. - $x ^ { 6 } = 9 x ^ { 4 }$

Factor the trinomial. - $25 y ^ { 3 } + 40 y ^ { 2 } + 16 y$

Find the function value. -If $P ( x ) = x ^ { 2 } + 7 x - 4$ , find $P ( 4 )$

Multiply. - $\left( 5.8 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 2 } \mathrm { z } \right) \left( 10 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 5 } \mathrm { z } ^ { 9 } \right)$

Multiply. - $\left( 5 x y ^ { 2 } + 12 x \right) \left( 5 x y ^ { 2 } - 12 x \right)$

Factor the trinomial. - $6 x ^ { 2 } - 26 x - 20$

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

For the given f(x $f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$ - $f ( x ) = x ^ { 2 } + 8 x + 7 ; g ( x ) = x + 2$

Simplify the polynomial by combining like terms. - $\left( 5 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 6 x y \right) + \left( 3 x ^ { 5 } y ^ { 3 } + 11 x ^ { 3 } y + 12 x y \right)$

Find the function. -If $P ( x ) = x - 6$ and $Q ( x ) = x ^ { 2 } - 11$ , find $P ( x ) \cdot Q ( x )$ .

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 5: Polynomials and Polynomial Functions

Divide. - (x2+15x+50)÷(x+5)\left( x ^ { 2 } + 15 x + 50 \right) \div ( x + 5 )(x2+15x+50)÷(x+5)

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with two terms.

Use substitution to factor the polynomial completely. - 15x4+19x2+615 x ^ { 4 } + 19 x ^ { 2 } + 615x4+19x2+6

Factor the polynomial. - x2+9x+14x ^ { 2 } + 9 x + 14x2+9x+14

Match the polynomial function with its graph. - f(x)=x(x−1)(x+1)f ( x ) = x ( x - 1 ) ( x + 1 )f(x)=x(x−1)(x+1)

Factor the polynomial completely. - x5−7x4−18x3x ^ { 5 } - 7 x ^ { 4 } - 18 x ^ { 3 }x5−7x4−18x3

Multiply. - (x−4)2( x - 4 ) ^ { 2 }(x−4)2

Divide. - (2x5−x3−4x2−12x+12)÷(x2−3)\left( 2 x ^ { 5 } - x ^ { 3 } - 4 x ^ { 2 } - 12 x + 12 \right) \div \left( x ^ { 2 } - 3 \right)(2x5−x3−4x2−12x+12)÷(x2−3)