Question 1

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
-$- 13 y ^ { 9 } - 2$

Accepted Answer

A)  9; binomial 
B)  -13; monomial 
C)  10; binomial 
D)  0; binomial 
A)  9; binomial 
B)  -13; monomial 
C)  10; binomial 
D)  0; binomial

Question 2

Multiply using the FOIL method.
-$( 2 y - 9 ) ( 3 y + 10 )$

Accepted Answer

A)  $6 y ^ { 2 } - 7 y - 90$ 
B)  $6 y ^ { 2 } - 90$ 
C)  $5 y ^ { 2 } + 1$ 
D)  $6 y ^ { 2 } + 47 y - 90$ 
A)  $6 y ^ { 2 } - 7 y - 90$ 
B)  $6 y ^ { 2 } - 90$ 
C)  $5 y ^ { 2 } + 1$ 
D)  $6 y ^ { 2 } + 47 y - 90$

Question 3

Multiply.
-$( 9 x - 1 ) \left( x ^ { 2 } - 3 x + 1 \right)$

Accepted Answer

A)  $9 x ^ { 3 } - 26 x ^ { 2 } + 6 x - 1$ 
B)  $9 x ^ { 3 } - 27 x ^ { 2 } + 9 x + 1$ 
C)  $9 x ^ { 3 } - 28 x ^ { 2 } + 12 x - 1$ 
D)  $9 x ^ { 3 } + 28 x ^ { 2 } - 12 x + 1$ 
A)  $9 x ^ { 3 } - 26 x ^ { 2 } + 6 x - 1$ 
B)  $9 x ^ { 3 } - 27 x ^ { 2 } + 9 x + 1$ 
C)  $9 x ^ { 3 } - 28 x ^ { 2 } + 12 x - 1$ 
D)  $9 x ^ { 3 } + 28 x ^ { 2 } - 12 x + 1$

Question 4

Multiply.
-$2 x ^ { 6 } \left( - 4 x ^ { 9 } \right)$

Accepted Answer

A)  $8 x ^ { 54 }$ 
B)  $- 8 x ^ { 15 }$ 
C)  $8 \times 15$ 
D)  $- 8 x ^ { 54 }$ 
A)  $8 x ^ { 54 }$ 
B)  $- 8 x ^ { 15 }$ 
C)  $8 \times 15$ 
D)  $- 8 x ^ { 54 }$

Question 5

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( \frac { p ^ { 7 } } { q ^ { 3 } } \right) ^ { 5 }$

Accepted Answer

A)  $\frac { p m 12 } { q ^ { 8 } }$ 
B)  $\frac { p ^ { 35 } } { q ^ { 15 } }$ 
C)  $\frac { p ^ { 5 } m ^ { 35 } } { q ^ { 15 } }$ 
D)  $\frac { \mathrm { p } ^ { 5 } \mathrm {~m} ^ { 12 } } { \mathrm { q } ^ { 8 } }$ 
A)  $\frac { p m 12 } { q ^ { 8 } }$ 
B)  $\frac { p ^ { 35 } } { q ^ { 15 } }$ 
C)  $\frac { p ^ { 5 } m ^ { 35 } } { q ^ { 15 } }$ 
D)  $\frac { \mathrm { p } ^ { 5 } \mathrm {~m} ^ { 12 } } { \mathrm { q } ^ { 8 } }$

Question 6

Simplify the expression. Write the result using positive exponents only.
-$r ^ { - 3 }$

Accepted Answer

A)  $r ^ { 1 / 3 }$ 
B)  $\frac { 1 } { \mathrm { r } ^ { 3 } }$ 
C)  $- \frac { 1 } { r ^ { 3 } }$ 
D)  $- r ^ { 3 }$ 
A)  $r ^ { 1 / 3 }$ 
B)  $\frac { 1 } { \mathrm { r } ^ { 3 } }$ 
C)  $- \frac { 1 } { r ^ { 3 } }$ 
D)  $- r ^ { 3 }$

Question 7

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

Accepted Answer

A)  $2 x ^ { 4 } + 4 x ^ { 3 } - 8 x ^ { 2 } + 8 x - 4$ 
B)  $2 x ^ { 4 } + 4 x ^ { 3 } - 6 x ^ { 2 } + 8 x - 4$ 
C)  $2 x ^ { 4 } + 2 x ^ { 3 } - 8 x ^ { 2 } + 8 x - 4$ 
D)  $2 x ^ { 4 } + 2 x ^ { 3 } - 6 x ^ { 2 } + 8 x - 4$ 
A)  $2 x ^ { 4 } + 4 x ^ { 3 } - 8 x ^ { 2 } + 8 x - 4$ 
B)  $2 x ^ { 4 } + 4 x ^ { 3 } - 6 x ^ { 2 } + 8 x - 4$ 
C)  $2 x ^ { 4 } + 2 x ^ { 3 } - 8 x ^ { 2 } + 8 x - 4$ 
D)  $2 x ^ { 4 } + 2 x ^ { 3 } - 6 x ^ { 2 } + 8 x - 4$

Question 8

Express the number in scientific notation.
-480,000

Accepted Answer

A)  $4.8 \times 10 ^ { - 4 }$ 
B)  $4.8 \times 10 ^ { - 5 }$ 
C)  $4.8 \times 10 ^ { 5 }$ 
D)  $4.8 \times 10 ^ { 4 }$ 
A)  $4.8 \times 10 ^ { - 4 }$ 
B)  $4.8 \times 10 ^ { - 5 }$ 
C)  $4.8 \times 10 ^ { 5 }$ 
D)  $4.8 \times 10 ^ { 4 }$

Question 9

Multiply vertically.
-$( 3 y - 2 ) ( 2 y + 9 )$

Accepted Answer

A)  $6 y ^ { 2 } + 31 y - 18$ 
B)  $6 y ^ { 2 } - 18$ 
C)  $5 y ^ { 2 } + 7$ 
D)  $6 y ^ { 2 } + 23 y - 18$ 
A)  $6 y ^ { 2 } + 31 y - 18$ 
B)  $6 y ^ { 2 } - 18$ 
C)  $5 y ^ { 2 } + 7$ 
D)  $6 y ^ { 2 } + 23 y - 18$

Question 10

Find the quotient using long division.
-$\frac { p ^ { 2 } + 4 p - 38 } { p + 9 }$

Accepted Answer

A)  $p - 5 + \frac { 7 } { p + 9 }$ 
B)  $p - 5$ 
C)  $p - 7 + \frac { 5 } { p + 9 }$ 
D)  $p + 5 + \frac { 7 } { p + 9 }$ 
A)  $p - 5 + \frac { 7 } { p + 9 }$ 
B)  $p - 5$ 
C)  $p - 7 + \frac { 5 } { p + 9 }$ 
D)  $p + 5 + \frac { 7 } { p + 9 }$

Question 11

Write the number in scientific notation.
-$0.00005345$

Accepted Answer

A)  $5.345 \times 10 ^ { 5 }$ 
B)  $5.345 \times 10 ^ { 4 }$ 
C)  $5.345 \times 10 ^ { - 4 }$ 
D)  $5.345 \times 10 ^ { - 5 }$ 
A)  $5.345 \times 10 ^ { 5 }$ 
B)  $5.345 \times 10 ^ { 4 }$ 
C)  $5.345 \times 10 ^ { - 4 }$ 
D)  $5.345 \times 10 ^ { - 5 }$

Question 12

Multiply.
-$2 x \left( 8 x ^ { 2 } - 3 x y + 4 y ^ { 2 } \right)$

Accepted Answer

A)  $16 x ^ { 3 } - 6 x y + 8 y ^ { 2 }$ 
B)  $16 x ^ { 3 } + 6 x ^ { 2 } y + 8 x y ^ { 2 }$ 
C)  $16 x ^ { 3 } y - 3 x y + 4 y ^ { 2 }$ 
D)  $16 x ^ { 3 } - 6 x ^ { 2 } y + 8 x y ^ { 2 }$ 
A)  $16 x ^ { 3 } - 6 x y + 8 y ^ { 2 }$ 
B)  $16 x ^ { 3 } + 6 x ^ { 2 } y + 8 x y ^ { 2 }$ 
C)  $16 x ^ { 3 } y - 3 x y + 4 y ^ { 2 }$ 
D)  $16 x ^ { 3 } - 6 x ^ { 2 } y + 8 x y ^ { 2 }$

Question 13

Simplify the expression.
-$( 6 a b ) ^ { 4 }$

Accepted Answer

A)  $1296 \mathrm { a } ^ { 4 } \mathrm {~b} ^ { 4 }$ 
B)  $6 a ^ { 4 } b ^ { 4 }$ 
C)  $10 a ^ { 4 } b ^ { 4 }$ 
D)  $24 a ^ { 4 } b ^ { 4 }$ 
A)  $1296 \mathrm { a } ^ { 4 } \mathrm {~b} ^ { 4 }$ 
B)  $6 a ^ { 4 } b ^ { 4 }$ 
C)  $10 a ^ { 4 } b ^ { 4 }$ 
D)  $24 a ^ { 4 } b ^ { 4 }$

Question 14

Perform the division.
-$\frac { 10 x ^ { 2 } + 6 x - 13 } { 2 x }$

Accepted Answer

A)  $5 x ^ { 2 } + 3 x - \frac { 13 } { 2 }$ 
B)  $10 x + 6 - \frac { 13 } { 2 x }$ 
C)  $5 x - 10$ 
D)  $5 x + 3 - \frac { 13 } { 2 x }$ 
A)  $5 x ^ { 2 } + 3 x - \frac { 13 } { 2 }$ 
B)  $10 x + 6 - \frac { 13 } { 2 x }$ 
C)  $5 x - 10$ 
D)  $5 x + 3 - \frac { 13 } { 2 x }$

Question 15

Solve.
-Use synthetic division to divide $\left( 5 x ^ { 4 } - 2 x ^ { 3 } + x - 3 \right)$ by $( x - 4 )$.

Accepted Answer

A)  $5 x ^ { 3 } + 18 x ^ { 2 } + 72 x + 289 + \frac { 1152 } { x - 4 }$ 
B)  $5 x ^ { 3 } + 18 x ^ { 2 } + 72 x + 289 + \frac { 1153 } { x - 4 }$ 
C)  $5 x ^ { 3 } - 18 x ^ { 2 } - 72 x - 289 - \frac { 1153 } { x - 4 }$ 
D)  $5 x ^ { 3 } + 20 x ^ { 2 } + 76 x + 313 + \frac { 1153 } { x - 4 }$ 
A)  $5 x ^ { 3 } + 18 x ^ { 2 } + 72 x + 289 + \frac { 1152 } { x - 4 }$ 
B)  $5 x ^ { 3 } + 18 x ^ { 2 } + 72 x + 289 + \frac { 1153 } { x - 4 }$ 
C)  $5 x ^ { 3 } - 18 x ^ { 2 } - 72 x - 289 - \frac { 1153 } { x - 4 }$ 
D)  $5 x ^ { 3 } + 20 x ^ { 2 } + 76 x + 313 + \frac { 1153 } { x - 4 }$

Question 16

Perform the division.
-$\frac { - 42 x ^ { 7 } - 30 x ^ { 6 } - 36 x ^ { 5 } } { - 6 x ^ { 6 } }$

Accepted Answer

A)  $7 x - 30 x ^ { 6 } + \frac { 6 } { x }$ 
B)  $7 x + 5$ 
C)  $7 x + 5 + \frac { 6 } { x }$ 
D)  $13 x + 5$ 
A)  $7 x - 30 x ^ { 6 } + \frac { 6 } { x }$ 
B)  $7 x + 5$ 
C)  $7 x + 5 + \frac { 6 } { x }$ 
D)  $13 x + 5$

Question 17

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

Accepted Answer

A)  $x ^ { 4 } - 64 y ^ { 2 }$ 
B)  $x ^ { 4 } - 16 x ^ { 2 } y - 64 y ^ { 2 }$ 
C)  $x ^ { 4 } - 16 y ^ { 2 }$ 
D)  $x ^ { 4 } + 16 x ^ { 2 } y - 64 y ^ { 2 }$ 
A)  $x ^ { 4 } - 64 y ^ { 2 }$ 
B)  $x ^ { 4 } - 16 x ^ { 2 } y - 64 y ^ { 2 }$ 
C)  $x ^ { 4 } - 16 y ^ { 2 }$ 
D)  $x ^ { 4 } + 16 x ^ { 2 } y - 64 y ^ { 2 }$

Question 18

Multiply.
-$( a - 3 ) \left( a ^ { 2 } + 3 a - 7 \right)$

Accepted Answer

A)  $a ^ { 3 } - 16 a + 21$ 
B)  $a ^ { 3 } + 6 a ^ { 2 } + 16 a - 21$ 
C)  $a ^ { 3 } + 2 a - 21$ 
D)  $a ^ { 3 } - 6 a ^ { 2 } - 16 a + 21$ 
A)  $a ^ { 3 } - 16 a + 21$ 
B)  $a ^ { 3 } + 6 a ^ { 2 } + 16 a - 21$ 
C)  $a ^ { 3 } + 2 a - 21$ 
D)  $a ^ { 3 } - 6 a ^ { 2 } - 16 a + 21$

Question 19

Simplify the exponential expression. Write the result using only positive exponents.
-$\frac { r ^ { - 6 } } { r ^ { - 4 } }$

Accepted Answer

A)  $\frac { 1 } { \mathrm { r } ^{10 }}$ 
B)  $\frac { 1 } { \mathrm { r } ^ { 2 } }$ 
C)  $\mathrm { r }^{ 10}$ 
D)  $r ^ { 2 }$ 
A)  $\frac { 1 } { \mathrm { r } ^{10 }}$ 
B)  $\frac { 1 } { \mathrm { r } ^ { 2 } }$ 
C)  $\mathrm { r }^{ 10}$ 
D)  $r ^ { 2 }$

Question 20

Simplify.
-If $P ( x ) = - 4 x - 3$ and $Q ( x ) = 2 x ^ { 2 } - 8 x - 5$, find $P ( x ) + Q ( x )$.

Accepted Answer

A)  $2 x ^ { 2 } - 12 x + 8$ 
B)  $2 x ^ { 2 } - 12 x - 8$ 
C)  $- 2 x ^ { 2 } - 12 x - 8$ 
D)  $2 x ^ { 2 } + 12 x - 8$ 
A)  $2 x ^ { 2 } - 12 x + 8$ 
B)  $2 x ^ { 2 } - 12 x - 8$ 
C)  $- 2 x ^ { 2 } - 12 x - 8$ 
D)  $2 x ^ { 2 } + 12 x - 8$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $- 13 y ^ { 9 } - 2$

Multiply using the FOIL method. - $( 2 y - 9 ) ( 3 y + 10 )$

Multiply. - $( 9 x - 1 ) \left( x ^ { 2 } - 3 x + 1 \right)$

Multiply. - $2 x ^ { 6 } \left( - 4 x ^ { 9 } \right)$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( \frac { p ^ { 7 } } { q ^ { 3 } } \right) ^ { 5 }$

Simplify the expression. Write the result using positive exponents only. - $r ^ { - 3 }$

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

Express the number in scientific notation. -480,000

Multiply vertically. - $( 3 y - 2 ) ( 2 y + 9 )$

Find the quotient using long division. - $\frac { p ^ { 2 } + 4 p - 38 } { p + 9 }$

Write the number in scientific notation. - $0.00005345$

Multiply. - $2 x \left( 8 x ^ { 2 } - 3 x y + 4 y ^ { 2 } \right)$

Simplify the expression. - $( 6 a b ) ^ { 4 }$

Perform the division. - $\frac { 10 x ^ { 2 } + 6 x - 13 } { 2 x }$

Solve. -Use synthetic division to divide $\left( 5 x ^ { 4 } - 2 x ^ { 3 } + x - 3 \right)$ by $( x - 4 )$ .

Perform the division. - $\frac { - 42 x ^ { 7 } - 30 x ^ { 6 } - 36 x ^ { 5 } } { - 6 x ^ { 6 } }$

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

Multiply. - $( a - 3 ) \left( a ^ { 2 } + 3 a - 7 \right)$

Simplify the exponential expression. Write the result using only positive exponents. - $\frac { r ^ { - 6 } } { r ^ { - 4 } }$

Simplify. -If $P ( x ) = - 4 x - 3$ and $Q ( x ) = 2 x ^ { 2 } - 8 x - 5$ , find $P ( x ) + Q ( x )$ .

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - −13y9−2- 13 y ^ { 9 } - 2−13y9−2

Multiply using the FOIL method. - (2y−9)(3y+10)( 2 y - 9 ) ( 3 y + 10 )(2y−9)(3y+10)

Multiply. - (9x−1)(x2−3x+1)( 9 x - 1 ) \left( x ^ { 2 } - 3 x + 1 \right)(9x−1)(x2−3x+1)

Multiply. - 2x6(−4x9)2 x ^ { 6 } \left( - 4 x ^ { 9 } \right)2x6(−4x9)

Use the power rule and the power of a product or quotient rule to simplify the expression. - (p7q3)5\left( \frac { p ^ { 7 } } { q ^ { 3 } } \right) ^ { 5 }(q3p7​)5

Simplify the expression. Write the result using positive exponents only. - r−3r ^ { - 3 }r−3

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