Question 1

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-$$- 5 x + 2$$

Accepted Answer

A)  binomial of degree 0 
B)  binomial of degree 2 
C)  monomial of degree 1 
D)  binomial of degree 1 
A)  binomial of degree 0 
B)  binomial of degree 2 
C)  monomial of degree 1 
D)  binomial of degree 1 D

Question 2

Divide.
-$$\left( 4 x ^ { 3 } + 18 x ^ { 2 } + 26 x - 18 \right) \div \left( x - \frac { 1 } { 2 } \right)$$

Accepted Answer

A)  $4 x ^ { 2 } + 20 x + 36$ 
B)  $4 x ^ { 2 } + 16 x + 18 + \frac { 4 } { x - \frac { 1 } { 2 } }$ 
C)  $4 x ^ { 2 } - 20 x + 36$ 
D)  $4 x ^ { 2 } + 20 x + 36 - \frac { 36 } { x - \frac { 1 } { 2 } }$ 
A)  $4 x ^ { 2 } + 20 x + 36$ 
B)  $4 x ^ { 2 } + 16 x + 18 + \frac { 4 } { x - \frac { 1 } { 2 } }$ 
C)  $4 x ^ { 2 } - 20 x + 36$ 
D)  $4 x ^ { 2 } + 20 x + 36 - \frac { 36 } { x - \frac { 1 } { 2 } }$ A

Question 3

Factor the polynomial completely.
-$384 x ^ { 3 } - 750$

Accepted Answer

A)  $6 ( 4 x - 5 ) \left( 16 x ^ { 2 } + 20 x + 25 \right)$ 
B)  $6 ( 4 x + 5 ) \left( 16 x ^ { 2 } - 20 x + 25 \right)$ 
C)  $6 \left( 64 x ^ { 3 } + 125 \right)$ 
D)  $6 ( 4 x + 5 ) \left( 16 x ^ { 2 } + 25 \right)$ 
A)  $6 ( 4 x - 5 ) \left( 16 x ^ { 2 } + 20 x + 25 \right)$ 
B)  $6 ( 4 x + 5 ) \left( 16 x ^ { 2 } - 20 x + 25 \right)$ 
C)  $6 \left( 64 x ^ { 3 } + 125 \right)$ 
D)  $6 ( 4 x + 5 ) \left( 16 x ^ { 2 } + 25 \right)$ A

Question 4

Perform the indicated operations and simplify.
-$$\left( 8 x ^ { 2 n } - x ^ { n } - 1 \right) + \left( x ^ { 2 n } + 9 x ^ { n } + 5 \right)$$

Accepted Answer

A)  $8 x ^ { 2 n } + 9 x ^ { n } + 5$ 
B)  $9 x ^ { 2 n } + 8 x ^ { n } + 4$ 
C)  $9 x ^ { 4 n } + 10 x ^ { 2 n } + 6$ 
D)  $7 x ^ { 4 n } - 10 x ^ { 2 n } - 6$ 
A)  $8 x ^ { 2 n } + 9 x ^ { n } + 5$ 
B)  $9 x ^ { 2 n } + 8 x ^ { n } + 4$ 
C)  $9 x ^ { 4 n } + 10 x ^ { 2 n } + 6$ 
D)  $7 x ^ { 4 n } - 10 x ^ { 2 n } - 6$

Question 5

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$$P ( x ) = 6 x ^ { 3 } + 3 x ^ { 2 } - x - 185 ; 3$$

Accepted Answer

A)  139 
B)  193 
C)  $- 29$ 
D)  1 
A)  139 
B)  193 
C)  $- 29$ 
D)  1

Question 6

Factor the polynomial completely.
-$48 x ^ { 3 } y + 42 x y ^ { 6 }$

Accepted Answer

A)  $6 y \left( 8 x ^ { 3 } + 7 x y ^ { 5 } \right)$ 
B)  $x y \left( 48 x ^ { 2 } + 42 y ^ { 5 } \right)$ 
C)  $6 x y \left( 8 x ^ { 2 } + 7 y ^ { 5 } \right)$ 
D)  $6 x \left( 8 x ^ { 2 } y + 7 y ^ { 6 } \right)$ 
A)  $6 y \left( 8 x ^ { 3 } + 7 x y ^ { 5 } \right)$ 
B)  $x y \left( 48 x ^ { 2 } + 42 y ^ { 5 } \right)$ 
C)  $6 x y \left( 8 x ^ { 2 } + 7 y ^ { 5 } \right)$ 
D)  $6 x \left( 8 x ^ { 2 } y + 7 y ^ { 6 } \right)$

Question 7

Factor the polynomial.
-$$6 x ^ { 2 } - 6 x + 54$$

Accepted Answer

A)  $6 \left( x ^ { 2 } - x + 9 \right)$ 
B)  $6 ( x + 1 ) ( x + 9 )$ 
C)  $6 \left( x ^ { 2 } + x + 9 \right)$ 
D)  prime polynomial 
A)  $6 \left( x ^ { 2 } - x + 9 \right)$ 
B)  $6 ( x + 1 ) ( x + 9 )$ 
C)  $6 \left( x ^ { 2 } + x + 9 \right)$ 
D)  prime polynomial

Question 8

Factor the polynomial.
-$x ( y + 6 ) - ( y + 6 )$

Accepted Answer

A)  $( y - 6 ) ( x - 1 )$ 
B)  $( y - 6 ) ( x + 1 )$ 
C)  $( y + 6 ) ( x - 1 )$ 
D)  $( y + 6 ) ( x + 1 )$ 
A)  $( y - 6 ) ( x - 1 )$ 
B)  $( y - 6 ) ( x + 1 )$ 
C)  $( y + 6 ) ( x - 1 )$ 
D)  $( y + 6 ) ( x + 1 )$

Question 9

Factor the polynomial by grouping.
-$24 x y + 20 x + 18 y + 15$

Accepted Answer

A)  $( 4 x + 3 ) ( 6 y + 5 )$ 
B)  $( 24 x - 3 ) ( y - 5 )$ 
C)  $( 24 x + 3 ) ( y + 5 )$ 
D)  $( 4 x - 3 ) ( 6 y - 5 )$ 
A)  $( 4 x + 3 ) ( 6 y + 5 )$ 
B)  $( 24 x - 3 ) ( y - 5 )$ 
C)  $( 24 x + 3 ) ( y + 5 )$ 
D)  $( 4 x - 3 ) ( 6 y - 5 )$

Question 10

Divide.
-$$\left( 5 x ^ { 2 } + 37 x - 72 \right) \div ( x + 9 )$$

Accepted Answer

A)  $5 x ^ { 2 } - 37$ 
B)  $5 x - 8$ 
C)  $x + 37$ 
D)  $5 x + 8$ 
A)  $5 x ^ { 2 } - 37$ 
B)  $5 x - 8$ 
C)  $x + 37$ 
D)  $5 x + 8$

Question 11

Subtract.
-$$\begin{array} { r } 
6 n ^ { 6 } + 6 n ^ { 3 } + 18 \
- \left( 4 n ^ { 6 } - 14 n ^ { 3 } - 13 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $2 n ^ { 6 } + 20 n ^ { 3 } + 5$ 
B)  $2 n ^ { 6 } + 20 n ^ { 3 } + 31$ 
C)  $53 n ^ { 9 }$ 
D)  $2 n ^ { 6 } + 10 n ^ { 3 } + 5$ 
A)  $2 n ^ { 6 } + 20 n ^ { 3 } + 5$ 
B)  $2 n ^ { 6 } + 20 n ^ { 3 } + 31$ 
C)  $53 n ^ { 9 }$ 
D)  $2 n ^ { 6 } + 10 n ^ { 3 } + 5$

Question 12

Divide.
-$$\frac { a ^ { 4 } b ^ { 5 } c + 4 a b c ^ { 3 } + 11 a ^ { 5 } b ^ { 8 } } { 2 a b c ^ { 3 } }$$

Accepted Answer

A)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 3 } } - 2 + \frac { 11 a ^ { 4 } b ^ { 7 } } { 2 c ^ { 3 } }$ 
B)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 2 } } + 2 + \frac { 11 a ^ { 4 } b ^ { 8 } } { 2 c ^ { 3 } }$ 
C)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 2 } } - 2 + \frac { 11 a ^ { 4 } b ^ { 7 } } { 2 c ^ { 3 } }$ 
D)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 2 } } + 2 + \frac { 11 a ^ { 4 } b ^ { 7 } } { 2 c ^ { 3 } }$ 
A)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 3 } } - 2 + \frac { 11 a ^ { 4 } b ^ { 7 } } { 2 c ^ { 3 } }$ 
B)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 2 } } + 2 + \frac { 11 a ^ { 4 } b ^ { 8 } } { 2 c ^ { 3 } }$ 
C)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 2 } } - 2 + \frac { 11 a ^ { 4 } b ^ { 7 } } { 2 c ^ { 3 } }$ 
D)  $\frac { a ^ { 3 } b ^ { 4 } } { 2 c ^ { 2 } } + 2 + \frac { 11 a ^ { 4 } b ^ { 7 } } { 2 c ^ { 3 } }$

Question 13

Solve.
-One number exceeds another number by 3, and their product is 154. Find the numbers.

Accepted Answer

A)  11 and 14, or -14 and -11 
B)  11 and 14 
C)  12 and 15 
D)  12 and 15, or -15 and -12 
A)  11 and 14, or -14 and -11 
B)  11 and 14 
C)  12 and 15 
D)  12 and 15, or -15 and -12

Question 14

Perform the indicated operations and simplify.
-$$\left( 8 x ^ { 5 } + 9 x ^ { 4 } \right) + \left( 5 x ^ { 5 } - 3 x ^ { 4 } \right)$$

Accepted Answer

A)  $19 x ^ { 9 }$ 
B)  $13 x ^ { 10 } + 6 x ^ { 8 }$ 
C)  $13 x ^ { 5 } + 6 x ^ { 4 }$ 
D)  $19 x ^ { 18 }$ 
A)  $19 x ^ { 9 }$ 
B)  $13 x ^ { 10 } + 6 x ^ { 8 }$ 
C)  $13 x ^ { 5 } + 6 x ^ { 4 }$ 
D)  $19 x ^ { 18 }$

Question 15

Factor the polynomial completely.
-$25 x ^ { 2 } - 36$

Accepted Answer

A)  $( 5 x + 6 ) ( 5 x - 6 )$ 
B)  $( 5 x - 6 ) ^ { 2 }$ 
C)  prime polynomial 
D)  $( 5 x + 6 ) ^ { 2 }$ 
A)  $( 5 x + 6 ) ( 5 x - 6 )$ 
B)  $( 5 x - 6 ) ^ { 2 }$ 
C)  prime polynomial 
D)  $( 5 x + 6 ) ^ { 2 }$

Question 16

Multiply.
-$$( x + 5 ) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 4 } + 5 x ^ { 3 } + 150 x ^ { 2 } + 250 x + 625$ 
B)  $x ^ { 4 } + 20 x ^ { 3 } + 150 x ^ { 2 } + 20 x + 625$ 
C)  $x ^ { 4 } + 20 x ^ { 3 } + 250 x ^ { 2 } + 500 x + 625$ 
D)  $x ^ { 4 } + 20 x ^ { 3 } + 150 x ^ { 2 } + 500 x + 625$ 
A)  $x ^ { 4 } + 5 x ^ { 3 } + 150 x ^ { 2 } + 250 x + 625$ 
B)  $x ^ { 4 } + 20 x ^ { 3 } + 150 x ^ { 2 } + 20 x + 625$ 
C)  $x ^ { 4 } + 20 x ^ { 3 } + 250 x ^ { 2 } + 500 x + 625$ 
D)  $x ^ { 4 } + 20 x ^ { 3 } + 150 x ^ { 2 } + 500 x + 625$

Question 17

Factor.
-$$( x - 5 ) ^ { 2 } - 4$$

Accepted Answer

A)  $( x - 3 ) ( x - 7 )$ 
B)  $( x + 3 ) ( x + 7 )$ 
C)  $( x - 1 ) ( x - 9 )$ 
D)  $( x - 7 ) ^ { 2 }$ 
A)  $( x - 3 ) ( x - 7 )$ 
B)  $( x + 3 ) ( x + 7 )$ 
C)  $( x - 1 ) ( x - 9 )$ 
D)  $( x - 7 ) ^ { 2 }$

Question 18

Perform the indicated operations and simplify.
-$$( 2 x - 8 ) + ( 8 x + 10 )$$

Accepted Answer

A)  $10 x + 2$ 
B)  $10 x ^ { 2 } + 2$ 
C)  $10 x - 2$ 
D)  $16 \mathrm { x } ^ { 2 } - 80$ 
A)  $10 x + 2$ 
B)  $10 x ^ { 2 } + 2$ 
C)  $10 x - 2$ 
D)  $16 \mathrm { x } ^ { 2 } - 80$

Question 19

Perform the indicated operations and simplify.
-$\left( 7 y ^ { 2 n } - 4 y ^ { n } + 2 \right) + \left( 4 y ^ { 2 n } + 2 y ^ { n } - 4 \right)$

Accepted Answer

A)  $6 y ^ { 2 n } + 9 y ^ { n } - 8$ 
B)  $7 y ^ { 3 n }$ 
C)  $11 y ^ { 4 n } - 2 y ^ { 2 n } - 2$ 
D)  $11 y ^ { 2 n } - 2 y ^ { n } - 2$ 
A)  $6 y ^ { 2 n } + 9 y ^ { n } - 8$ 
B)  $7 y ^ { 3 n }$ 
C)  $11 y ^ { 4 n } - 2 y ^ { 2 n } - 2$ 
D)  $11 y ^ { 2 n } - 2 y ^ { n } - 2$

Question 20

Solve.
-If the area of a rectangle is $\left( 2 x ^ { 4 } + 11 x ^ { 3 } - 10 x ^ { 2 } - 93 x - 90 \right)$ square inches, and its width is $( 2 x + 3 )$ inches, find its length.

Accepted Answer

A)  $x ^ { 3 } + 4 x ^ { 2 } - 11 x - 30$ in. 
B)  $x ^ { 3 } - 10 x ^ { 2 } + 5 x - 30$ in. 
C)  $x ^ { 3 } - 11 x ^ { 2 } + 4 x - 30$ in. 
D)  $x ^ { 3 } + 5 x ^ { 2 } - 10 x - 30$ in. 
A)  $x ^ { 3 } + 4 x ^ { 2 } - 11 x - 30$ in. 
B)  $x ^ { 3 } - 10 x ^ { 2 } + 5 x - 30$ in. 
C)  $x ^ { 3 } - 11 x ^ { 2 } + 4 x - 30$ in. 
D)  $x ^ { 3 } + 5 x ^ { 2 } - 10 x - 30$ in.

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - $- 5 x + 2$

Divide. - $\left( 4 x ^ { 3 } + 18 x ^ { 2 } + 26 x - 18 \right) \div \left( x - \frac { 1 } { 2 } \right)$

Factor the polynomial completely. - $384 x ^ { 3 } - 750$

Perform the indicated operations and simplify. - $\left( 8 x ^ { 2 n } - x ^ { n } - 1 \right) + \left( x ^ { 2 n } + 9 x ^ { n } + 5 \right)$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = 6 x ^ { 3 } + 3 x ^ { 2 } - x - 185 ; 3$

Factor the polynomial completely. - $48 x ^ { 3 } y + 42 x y ^ { 6 }$

Factor the polynomial. - $6 x ^ { 2 } - 6 x + 54$

Factor the polynomial. - $x ( y + 6 ) - ( y + 6 )$

Factor the polynomial by grouping. - $24 x y + 20 x + 18 y + 15$

Divide. - $\left( 5 x ^ { 2 } + 37 x - 72 \right) \div ( x + 9 )$

Subtract. - 6+6+18 - 4-14-13

Divide. - $\frac { a ^ { 4 } b ^ { 5 } c + 4 a b c ^ { 3 } + 11 a ^ { 5 } b ^ { 8 } } { 2 a b c ^ { 3 } }$

Solve. -One number exceeds another number by 3, and their product is 154. Find the numbers.

Perform the indicated operations and simplify. - $\left( 8 x ^ { 5 } + 9 x ^ { 4 } \right) + \left( 5 x ^ { 5 } - 3 x ^ { 4 } \right)$

Factor the polynomial completely. - $25 x ^ { 2 } - 36$

Multiply. - $( x + 5 ) ^ { 4 }$

Factor. - $( x - 5 ) ^ { 2 } - 4$

Perform the indicated operations and simplify. - $( 2 x - 8 ) + ( 8 x + 10 )$

Perform the indicated operations and simplify. - $\left( 7 y ^ { 2 n } - 4 y ^ { n } + 2 \right) + \left( 4 y ^ { 2 n } + 2 y ^ { n } - 4 \right)$

Solve. -If the area of a rectangle is $\left( 2 x ^ { 4 } + 11 x ^ { 3 } - 10 x ^ { 2 } - 93 x - 90 \right)$ square inches, and its width is $( 2 x + 3 )$ inches, find its length.

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

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - −5x+2- 5 x + 2−5x+2

Divide. - (4x3+18x2+26x−18)÷(x−12)\left( 4 x ^ { 3 } + 18 x ^ { 2 } + 26 x - 18 \right) \div \left( x - \frac { 1 } { 2 } \right)(4x3+18x2+26x−18)÷(x−21​)

Factor the polynomial completely. - 384x3−750384 x ^ { 3 } - 750384x3−750

Perform the indicated operations and simplify. - (8x2n−xn−1)+(x2n+9xn+5)\left( 8 x ^ { 2 n } - x ^ { n } - 1 \right) + \left( x ^ { 2 n } + 9 x ^ { n } + 5 \right)(8x2n−xn−1)+(x2n+9xn+5)

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=6x3+3x2−x−185;3P ( x ) = 6 x ^ { 3 } + 3 x ^ { 2 } - x - 185 ; 3P(x)=6x3+3x2−x−185;3

Factor the polynomial completely. - 48x3y+42xy648 x ^ { 3 } y + 42 x y ^ { 6 }48x3y+42xy6

Factor the polynomial. - 6x2−6x+546 x ^ { 2 } - 6 x + 546x2−6x+54

Factor the polynomial. - x(y+6)−(y+6)x ( y + 6 ) - ( y + 6 )x(y+6)−(y+6)

Factor the polynomial by grouping. - 24xy+20x+18y+1524 x y + 20 x + 18 y + 1524xy+20x+18y+15

Divide. - (5x2+37x−72)÷(x+9)\left( 5 x ^ { 2 } + 37 x - 72 \right) \div ( x + 9 )(5x2+37x−72)÷(x+9)