Question 1

Multiply.
-$$\begin{array} { r } 
3 x + 5 \
\times 2 x + 1 \
\hline
\end{array}$$

Accepted Answer

A)  $5 x ^ { 2 } + 6$ 
B)  $6 x ^ { 2 } + 13 x + 5$ 
C)  $6 x ^ { 2 } + 5$ 
D)  $6 x ^ { 2 } - 7 x + 5$ 
A)  $5 x ^ { 2 } + 6$ 
B)  $6 x ^ { 2 } + 13 x + 5$ 
C)  $6 x ^ { 2 } + 5$ 
D)  $6 x ^ { 2 } - 7 x + 5$

Question 2

Solve the equation.
-$$( x + 6 ) ( x - 5 ) ( x - 18 ) = 0$$

Accepted Answer

A)  $\{ - 6,5 , - 18 \}$ 
B)  $\{ 0 , - 6,5 \}$ 
C)  $\{ 6,5,18 \}$ 
D)  $\{ - 6,5,18 \}$ 
A)  $\{ - 6,5 , - 18 \}$ 
B)  $\{ 0 , - 6,5 \}$ 
C)  $\{ 6,5,18 \}$ 
D)  $\{ - 6,5,18 \}$

Question 3

Solve the equation.
-$$\frac { 5 x ^ { 2 } } { 11 } - \frac { 29 x } { 77 } + \frac { 6 } { 77 } = 0$$

Accepted Answer

A)  $\{ 3,2 \}$ 
B)  $\left\{ \frac { 3 } { 7 } , \frac { 2 } { 5 } \right\}$ 
C)  $\{ - 3 , - 2 \}$ 
D)  $\left\{ - \frac { 3 } { 7 } , - \frac { 2 } { 5 } \right\}$ 
A)  $\{ 3,2 \}$ 
B)  $\left\{ \frac { 3 } { 7 } , \frac { 2 } { 5 } \right\}$ 
C)  $\{ - 3 , - 2 \}$ 
D)  $\left\{ - \frac { 3 } { 7 } , - \frac { 2 } { 5 } \right\}$

Question 4

Factor completely.
-$2 x y ^ { 2 } - 98 x$

Accepted Answer

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

Question 5

Factor.
-$25 x ^ { 2 } + 90 x y + 81 y ^ { 2 }$

Accepted Answer

A)  $( 5 x + 9 y ) ( 5 x - 9 y )$ 
B)  $( 5 x - 9 y ) ^ { 2 }$ 
C)  $( 5 x + 9 y ) ^ { 2 }$ 
D)  $( 25 x + y ) ( x + 81 y )$ 
A)  $( 5 x + 9 y ) ( 5 x - 9 y )$ 
B)  $( 5 x - 9 y ) ^ { 2 }$ 
C)  $( 5 x + 9 y ) ^ { 2 }$ 
D)  $( 25 x + y ) ( x + 81 y )$

Question 6

Subtract.
-$$\begin{array} { r } 
x ^ { 4 } + 8 x ^ { 3 } \
- \left( 15 x ^ { 4 } + 13 x ^ { 3 } \right) \
\hline
\end{array}$$

Accepted Answer

A)  $- 14 x ^ { 4 } - 5 x ^ { 3 }$ 
B)  $34 x ^ { 4 } + 21 x ^ { 3 }$ 
C)  $- 14 x ^ { 4 } + 21 x ^ { 3 }$ 
D)  $- 19 x ^ { 7 }$ 
A)  $- 14 x ^ { 4 } - 5 x ^ { 3 }$ 
B)  $34 x ^ { 4 } + 21 x ^ { 3 }$ 
C)  $- 14 x ^ { 4 } + 21 x ^ { 3 }$ 
D)  $- 19 x ^ { 7 }$

Question 7

Factor.
-$27 x ^ { 3 } + 1$

Accepted Answer

A)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x - 1 \right)$ 
B)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 3 x + 1 \right)$ 
C)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x + 1 \right)$ 
D)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 1 \right)$ 
A)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x - 1 \right)$ 
B)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 3 x + 1 \right)$ 
C)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x + 1 \right)$ 
D)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 1 \right)$

Question 8

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$$P ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 12 x - 64 ; 2$$

Accepted Answer

A)  $- 232$ 
B)  4 
C)  8 
D)  $- 64$ 
A)  $- 232$ 
B)  4 
C)  8 
D)  $- 64$

Question 9

Subtract.
-$$\left( 8 x ^ { 2 n } + 13 x ^ { n } + 7 \right) - \left( 4 x ^ { 2 n } + 9 x ^ { n } + 13 \right)$$

Accepted Answer

A)  $4 x ^ { 2 n } + 17 x ^ { n } + 20$ 
B)  $4 x ^ { 2 n } + 4 x ^ { n } + 20$ 
C)  $4 x ^ { 2 n } + 4 x ^ { n } - 6$ 
D)  $4 x ^ { 4 n } + 4 x ^ { 2 n } - 6$ 
A)  $4 x ^ { 2 n } + 17 x ^ { n } + 20$ 
B)  $4 x ^ { 2 n } + 4 x ^ { n } + 20$ 
C)  $4 x ^ { 2 n } + 4 x ^ { n } - 6$ 
D)  $4 x ^ { 4 n } + 4 x ^ { 2 n } - 6$

Question 10

Solve.
-If the volume of a box is $\left( 30 x ^ { 3 } + 32 x ^ { 2 } - 30 x \right)$ cubic centimeters, its height is $2 x$ centimeters, and its length is $( 3 x$ +5) centimeters, find its width.

Accepted Answer

A)  $( 5 x + 6 ) \mathrm { cm }$ 
B)  $( 5 x - 6 ) \mathrm { cm }$ 
C)  $( 5 x - 3 ) \mathrm { cm }$ 
D)  $( 5 x + 3 ) \mathrm { cm }$ 
A)  $( 5 x + 6 ) \mathrm { cm }$ 
B)  $( 5 x - 6 ) \mathrm { cm }$ 
C)  $( 5 x - 3 ) \mathrm { cm }$ 
D)  $( 5 x + 3 ) \mathrm { cm }$

Question 11

Subtract.
-$$\left( 3 y ^ { 2 n } + 6 y ^ { n } - 1 \right) - \left( 4 y ^ { 2 n } + 3 y ^ { n } + 6 \right)$$

Accepted Answer

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

Question 12

Use substitution to factor the polynomial completely.
-$$( x + 7 ) ^ { 2 } - 10 ( x + 7 ) + 16$$

Accepted Answer

A)  $\left( x ^ { 2 } - 7 x + 8 \right) \left( x ^ { 2 } - 7 x + 2 \right)$ 
B)  $\left( x ^ { 2 } + 7 x - 8 \right) \left( x ^ { 2 } + 7 x - 2 \right)$ 
C)  $( x + 15 ) ( x + 9 )$ 
D)  $( x - 1 ) ( x + 5 )$ 
A)  $\left( x ^ { 2 } - 7 x + 8 \right) \left( x ^ { 2 } - 7 x + 2 \right)$ 
B)  $\left( x ^ { 2 } + 7 x - 8 \right) \left( x ^ { 2 } + 7 x - 2 \right)$ 
C)  $( x + 15 ) ( x + 9 )$ 
D)  $( x - 1 ) ( x + 5 )$

Question 13

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

-The is the sum of the exponents on the variables contained in the term.

Accepted Answer

A) factoring 
B)  degree of a term 
C)  degree of a polynomial 
D)  FOIL 
A) factoring 
B)  degree of a term 
C)  degree of a polynomial 
D)  FOIL

Question 14

Multiply.
-$$[ 4 x + ( 2 y - 1 ) ] ^ { 2 }$$

Accepted Answer

A)  $16 x ^ { 2 } - 8 x y + 1$ 
B)  $16 x ^ { 2 } + 16 x y - 8 x + 4 y ^ { 2 } - 4 y + 1$ 
C)  $16 x ^ { 2 } + 4 y ^ { 2 } + 1$ 
D)  $16 x ^ { 2 } - 16 x y + 1$ 
A)  $16 x ^ { 2 } - 8 x y + 1$ 
B)  $16 x ^ { 2 } + 16 x y - 8 x + 4 y ^ { 2 } - 4 y + 1$ 
C)  $16 x ^ { 2 } + 4 y ^ { 2 } + 1$ 
D)  $16 x ^ { 2 } - 16 x y + 1$

Question 15

Multiply.
-$$\left( x + \frac { 1 } { 9 } \right) \left( x - \frac { 1 } { 9 } \right)$$

Accepted Answer

A)  $x ^ { 2 } - \frac { 2 } { 9 } x - \frac { 1 } { 81 }$ 
B)  $x ^ { 2 } + \frac { 2 } { 9 } x - \frac { 1 } { 81 }$ 
C)  $x ^ { 2 } - 1$ 
D)  $x ^ { 2 } - \frac { 1 } { 81 }$ 
A)  $x ^ { 2 } - \frac { 2 } { 9 } x - \frac { 1 } { 81 }$ 
B)  $x ^ { 2 } + \frac { 2 } { 9 } x - \frac { 1 } { 81 }$ 
C)  $x ^ { 2 } - 1$ 
D)  $x ^ { 2 } - \frac { 1 } { 81 }$

Question 16

Find the degree of the term.
$- 5 x ^ { 4 }$

Accepted Answer

A)  1 
B)   -5 
C)  4 
D)  no degree 
A)  1 
B)   -5 
C)  4 
D)  no degree

Question 17

Factor the trinomial.
-$$12 x ^ { 2 } + 54 x - 30$$

Accepted Answer

A)  $6 ( 2 x - 1 ) ( x + 5 )$ 
B)  $( 12 x - 6 ) ( x + 5 )$ 
C)  $6 ( 2 x + 1 ) ( x - 5 )$ 
D)  prime polynomial 
A)  $6 ( 2 x - 1 ) ( x + 5 )$ 
B)  $( 12 x - 6 ) ( x + 5 )$ 
C)  $6 ( 2 x + 1 ) ( x - 5 )$ 
D)  prime polynomial

Question 18

Factor the polynomial completely.
-$$36 y ^ { 2 } - 60 y + 25$$

Accepted Answer

A)  $( 36 y + 1 ) ( y + 25 )$ 
B)  $( 6 y - 5 ) ^ { 2 }$ 
C)  $( 6 y + 5 ) ^ { 2 }$ 
D)  $( 6 y - 5 ) ( 6 y + 5 )$ 
A)  $( 36 y + 1 ) ( y + 25 )$ 
B)  $( 6 y - 5 ) ^ { 2 }$ 
C)  $( 6 y + 5 ) ^ { 2 }$ 
D)  $( 6 y - 5 ) ( 6 y + 5 )$

Question 19

Perform the indicated operations and simplify.
-$$\left( 7 x ^ { 4 } + 7 x ^ { 3 } - 2 x ^ { 2 } - 2 \right) + \left( 3 x ^ { 4 } - 2 x ^ { 3 } - 6 x ^ { 2 } - 9 \right)$$

Accepted Answer

A)  $10 x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } + 10$ 
B)  $10 x ^ { 4 } + 5 x ^ { 3 } - 8 x ^ { 2 } - 11$ 
C)  $7 x ^ { 18 } - 11$ 
D)  $10 x ^ { 8 } + 5 x ^ { 6 } - 8 x ^ { 4 } - 11$ 
A)  $10 x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } + 10$ 
B)  $10 x ^ { 4 } + 5 x ^ { 3 } - 8 x ^ { 2 } - 11$ 
C)  $7 x ^ { 18 } - 11$ 
D)  $10 x ^ { 8 } + 5 x ^ { 6 } - 8 x ^ { 4 } - 11$

Question 20

Subtract.
-Subtract $( 3 x - 30 )$ from the sum of $( - 2 x + 12 )$ and $( 9 x - 1 )$.

Accepted Answer

A)  $4 x + 41$ 
B)  $10 x - 19$ 
C)  $- 4 x - 41$ 
D)  $8 x + 43$ 
A)  $4 x + 41$ 
B)  $10 x - 19$ 
C)  $- 4 x - 41$ 
D)  $8 x + 43$

Multiply. - 3x+5 \times2x+1

Solve the equation. - $( x + 6 ) ( x - 5 ) ( x - 18 ) = 0$

Solve the equation. - $\frac { 5 x ^ { 2 } } { 11 } - \frac { 29 x } { 77 } + \frac { 6 } { 77 } = 0$

Factor completely. - $2 x y ^ { 2 } - 98 x$

Factor. - $25 x ^ { 2 } + 90 x y + 81 y ^ { 2 }$

Subtract. - +8 - 15+13

Factor. - $27 x ^ { 3 } + 1$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 12 x - 64 ; 2$

Subtract. - $\left( 8 x ^ { 2 n } + 13 x ^ { n } + 7 \right) - \left( 4 x ^ { 2 n } + 9 x ^ { n } + 13 \right)$

Subtract. - $\left( 3 y ^ { 2 n } + 6 y ^ { n } - 1 \right) - \left( 4 y ^ { 2 n } + 3 y ^ { n } + 6 \right)$

Use substitution to factor the polynomial completely. - $( x + 7 ) ^ { 2 } - 10 ( x + 7 ) + 16$

Fill in the blank with one of the words or phrases listed below. -The is the sum of the exponents on the variables contained in the term.

Multiply. - $[ 4 x + ( 2 y - 1 ) ] ^ { 2 }$

Multiply. - $\left( x + \frac { 1 } { 9 } \right) \left( x - \frac { 1 } { 9 } \right)$

Find the degree of the term. $- 5 x ^ { 4 }$

Factor the trinomial. - $12 x ^ { 2 } + 54 x - 30$

Factor the polynomial completely. - $36 y ^ { 2 } - 60 y + 25$

Perform the indicated operations and simplify. - $\left( 7 x ^ { 4 } + 7 x ^ { 3 } - 2 x ^ { 2 } - 2 \right) + \left( 3 x ^ { 4 } - 2 x ^ { 3 } - 6 x ^ { 2 } - 9 \right)$

Subtract. -Subtract $( 3 x - 30 )$ from the sum of $( - 2 x + 12 )$ and $( 9 x - 1 )$ .

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

Multiply. - 3x+5 \times2x+1

Solve the equation. - (x+6)(x−5)(x−18)=0( x + 6 ) ( x - 5 ) ( x - 18 ) = 0(x+6)(x−5)(x−18)=0

Solve the equation. - 5x211−29x77+677=0\frac { 5 x ^ { 2 } } { 11 } - \frac { 29 x } { 77 } + \frac { 6 } { 77 } = 0115x2​−7729x​+776​=0

Factor completely. - 2xy2−98x2 x y ^ { 2 } - 98 x2xy2−98x

Factor. - 25x2+90xy+81y225 x ^ { 2 } + 90 x y + 81 y ^ { 2 }25x2+90xy+81y2

Subtract. - +8 - 15+13

Factor. - 27x3+127 x ^ { 3 } + 127x3+1

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=x4+6x3−4x2+12x−64;2P ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 12 x - 64 ; 2P(x)=x4+6x3−4x2+12x−64;2

Subtract. - (8x2n+13xn+7)−(4x2n+9xn+13)\left( 8 x ^ { 2 n } + 13 x ^ { n } + 7 \right) - \left( 4 x ^ { 2 n } + 9 x ^ { n } + 13 \right)(8x2n+13xn+7)−(4x2n+9xn+13)

Solve. -If the volume of a box is (30x3+32x2−30x)\left( 30 x ^ { 3 } + 32 x ^ { 2 } - 30 x \right)(30x3+32x2−30x) cubic centimeters, its height is 2x2 x2x centimeters, and its length is (3x( 3 x(3x +5) centimeters, find its width.

Subtract. - (3y2n+6yn−1)−(4y2n+3yn+6)\left( 3 y ^ { 2 n } + 6 y ^ { n } - 1 \right) - \left( 4 y ^ { 2 n } + 3 y ^ { n } + 6 \right)(3y2n+6yn−1)−(4y2n+3yn+6)

Use substitution to factor the polynomial completely. - (x+7)2−10(x+7)+16( x + 7 ) ^ { 2 } - 10 ( x + 7 ) + 16(x+7)2−10(x+7)+16