Question 1

Find the quotient using long division.
-$\frac { 6 m ^ { 3 } + 25 m ^ { 2 } - 21 m + 20 } { m + 5 }$

Accepted Answer

A)  $6 m ^ { 2 } - 5 m + 4$ 
B)  $m ^ { 2 } + 6 m + 7$ 
C)  $m ^ { 2 } + 5 m + 6$ 
D)  $6 \mathrm {~m} ^ { 2 } + 5 \mathrm {~m} + 4$ 
A)  $6 m ^ { 2 } - 5 m + 4$ 
B)  $m ^ { 2 } + 6 m + 7$ 
C)  $m ^ { 2 } + 5 m + 6$ 
D)  $6 \mathrm {~m} ^ { 2 } + 5 \mathrm {~m} + 4$

Question 2

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( 3 a ^ { 3 } b \right) ^ { 2 }$

Accepted Answer

A)  $3 a ^ { 5 } b ^ { 2 }$ 
B)  $9 a ^ { 5 } b ^ { 2 }$ 
C)  $3 a ^ { 6 } b ^ { 2 }$ 
D)  $9 a ^ { 6 } b ^ { 2 }$ 
A)  $3 a ^ { 5 } b ^ { 2 }$ 
B)  $9 a ^ { 5 } b ^ { 2 }$ 
C)  $3 a ^ { 6 } b ^ { 2 }$ 
D)  $9 a ^ { 6 } b ^ { 2 }$

Question 3

Simplify.
-If $P ( x ) = - 9 x ^ { 2 } - 4 x$, find $P ( - 3 )$.

Accepted Answer

A)  $- 88$ 
B)  39 
C)  $- 69$ 
D)  $- 81$ 
A)  $- 88$ 
B)  39 
C)  $- 69$ 
D)  $- 81$

Question 4

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

Accepted Answer

A)  $x ^ { 2 } + 19 x y + 19 y ^ { 2 }$ 
B)  $x + 19 x y + 90 y$ 
C)  $x ^ { 2 } + 16 x y + 90 y ^ { 2 }$ 
D)  $x ^ { 2 } + 19 x y + 90 y ^ { 2 }$ 
A)  $x ^ { 2 } + 19 x y + 19 y ^ { 2 }$ 
B)  $x + 19 x y + 90 y$ 
C)  $x ^ { 2 } + 16 x y + 90 y ^ { 2 }$ 
D)  $x ^ { 2 } + 19 x y + 90 y ^ { 2 }$

Question 5

Simplify the expression. Write the result using positive exponents only.
-$\frac { p ^ { 6 } } { p ^ { - 8 } }$

Accepted Answer

A)  $\frac { 1 } { p ^ { 48 } }$ 
B)  $\frac { 1 } { p ^ { 14 } }$ 
C)  $p ^ { 48 }$ 
D)  $p ^ { 14 }$ 
A)  $\frac { 1 } { p ^ { 48 } }$ 
B)  $\frac { 1 } { p ^ { 14 } }$ 
C)  $p ^ { 48 }$ 
D)  $p ^ { 14 }$

Question 6

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
-$23 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 14 q ^ { 2 } s$

Accepted Answer

A)  3; none of these 
B)  3; trinomial 
C)  4; none of these 
D)  4; trinomial 
A)  3; none of these 
B)  3; trinomial 
C)  4; none of these 
D)  4; trinomial

Question 7

Simplify the expression.
-$5 ^ { 2 } + 5 ^ { 3 }$

Accepted Answer

A)  15,625 
B)  3125 
C)  150 
D)  25 
A)  15,625 
B)  3125 
C)  150 
D)  25

Question 8

Perform the indicated operation.
-Subtract $( 22 x + 6 )$ from $\left( - 2 x ^ { 2 } - 11 x + 6 \right)$

Accepted Answer

A)  $- 2 x ^ { 2 } - 33 x$ 
B)  $2 x ^ { 2 } + 33 x$ 
C)  $- 2 x ^ { 2 } - 33 x - 12$ 
D)  $- 2 x ^ { 2 } + 11 x + 12$ 
A)  $- 2 x ^ { 2 } - 33 x$ 
B)  $2 x ^ { 2 } + 33 x$ 
C)  $- 2 x ^ { 2 } - 33 x - 12$ 
D)  $- 2 x ^ { 2 } + 11 x + 12$

Question 9

Express the number in scientific notation.
-$0.000015717$

Accepted Answer

A)  $1.5717 \times 10 ^ { - 5 }$ 
B)  $1.5717 \times 10 ^ { - 4 }$ 
C)  $1.5717 \times 10 ^ { 4 }$ 
D)  $1.5717 \times 10 ^ { 5 }$ 
A)  $1.5717 \times 10 ^ { - 5 }$ 
B)  $1.5717 \times 10 ^ { - 4 }$ 
C)  $1.5717 \times 10 ^ { 4 }$ 
D)  $1.5717 \times 10 ^ { 5 }$

Question 10

Perform the indicated operation.
-$\left( 2 y ^ { 5 } - 7 y ^ { 4 } - 2 \right) + \left( 7 y ^ { 5 } - 9 y ^ { 4 } + 2 \right)$

Accepted Answer

A)  - 7 y18 
B)  $- 7 y ^ { 9 }$ 
C)  $9 y ^ { 5 } - 16 y ^ { 4 }$ 
D)  $9 \mathrm { y } ^ { 10 } - 16 \mathrm { y } ^ { 8 }$ 
A)  - 7 y18 
B)  $- 7 y ^ { 9 }$ 
C)  $9 y ^ { 5 } - 16 y ^ { 4 }$ 
D)  $9 \mathrm { y } ^ { 10 } - 16 \mathrm { y } ^ { 8 }$

Question 11

Perform the indicated operation.
-$5 x ^ { 3 } + 6 x ^ { 2 } + 7 x + 5 - \left( 2 x ^ { 3 } - 4 x ^ { 2 } - 9 x + 2 \right)$

Accepted Answer

A)  $3 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 7$ 
B)  $7 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 7$ 
C)  $3 x ^ { 3 } + 10 x ^ { 2 } + 16 x + 3$ 
D)  $7 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$ 
A)  $3 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 7$ 
B)  $7 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 7$ 
C)  $3 x ^ { 3 } + 10 x ^ { 2 } + 16 x + 3$ 
D)  $7 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$

Question 12

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

Accepted Answer

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

Question 13

Use the product rule to simplify the expression. Write the result using exponents.
-$2 ^ { 5 } \cdot 2 ^ { 4 }$

Accepted Answer

A)  $2 ^ { 9 }$ 
B)   $2 ^ {20 }$ 
C)  $4^ { 20 }$ 
D)  $4 ^ { 9 }$ 
A)  $2 ^ { 9 }$ 
B)   $2 ^ {20 }$ 
C)  $4^ { 20 }$ 
D)  $4 ^ { 9 }$

Question 14

Evaluate the expression with the given replacement values.
-$4 x ^ { 2 } ; x = 6$

Accepted Answer

A)  96 
B)  48 
C)  144 
D)  576 
A)  96 
B)  48 
C)  144 
D)  576

Question 15

Complete the table for the polynomial and answer the question.
-$9 x y^{2}-7 x^{6} y^{6} z+2 x^{3} y-2$
 
$\text { What is the degree of the polynomial? }$

Accepted Answer

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

Question 16

Simplify by combining like terms.
-$5 x ^ { 2 } + 3 x y - 9 x ^ { 2 } + 14 + 2 x y$

Accepted Answer

A)  $5 x ^ { 2 } + 5 x y - 14$ 
B)  $- 4 x ^ { 2 } - 5 x y + 14$ 
C)  $- 4 x ^ { 2 } + 5 x y + 14$ 
D)  $5 x ^ { 2 } + 5 x y + 14$ 
A)  $5 x ^ { 2 } + 5 x y - 14$ 
B)  $- 4 x ^ { 2 } - 5 x y + 14$ 
C)  $- 4 x ^ { 2 } + 5 x y + 14$ 
D)  $5 x ^ { 2 } + 5 x y + 14$

Question 17

Find the quotient using long division.
-$\frac { x ^ { 2 } - 9 } { x + 3 }$

Accepted Answer

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

Question 18

Solve.
-The rectangle has width $7 x ^ { 3 }$ feet and length $8 x ^ { 4 }$ feet. Find its area as an expression in $x$. $($ Area $=$ length $\cdot$ width $)$

Accepted Answer

A)  $56 \mathrm { x } ^ { 7 } \mathrm { sq } \mathrm { ft }$ 
B)  $15 \mathrm { x } ^ { 12 } \mathrm { sq } \mathrm { ft }$ 
C)  $15 x ^ { 7 } s q f t$ 
D)  $56 \mathrm { x } ^ { 12 } \mathrm { sq } \mathrm { ft }$ 
A)  $56 \mathrm { x } ^ { 7 } \mathrm { sq } \mathrm { ft }$ 
B)  $15 \mathrm { x } ^ { 12 } \mathrm { sq } \mathrm { ft }$ 
C)  $15 x ^ { 7 } s q f t$ 
D)  $56 \mathrm { x } ^ { 12 } \mathrm { sq } \mathrm { ft }$

Question 19

Evaluate the expression.
-$3^3$

Accepted Answer

A)  27 
B)  -9 
C)  -27 
D)  9 
A)  27 
B)  -9 
C)  -27 
D)  9

Question 20

Use the product rule to simplify the expression. Write the result using exponents.
-$\left( 8 p ^ { 9 } \right) \left( - 7 p ^ { 8 } \right)$

Accepted Answer

A)  $56 \mathrm { p } ^ { 72 }$ 
B)  $56 p ^ { 17 }$ 
C)  $- 56 p ^ { 72 }$ 
D)  $- 56 p ^ { 17 }$ 
A)  $56 \mathrm { p } ^ { 72 }$ 
B)  $56 p ^ { 17 }$ 
C)  $- 56 p ^ { 72 }$ 
D)  $- 56 p ^ { 17 }$

Find the quotient using long division. - $\frac { 6 m ^ { 3 } + 25 m ^ { 2 } - 21 m + 20 } { m + 5 }$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( 3 a ^ { 3 } b \right) ^ { 2 }$

Simplify. -If $P ( x ) = - 9 x ^ { 2 } - 4 x$ , find $P ( - 3 )$ .

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

Simplify the expression. Write the result using positive exponents only. - $\frac { p ^ { 6 } } { p ^ { - 8 } }$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $23 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 14 q ^ { 2 } s$

Simplify the expression. - $5 ^ { 2 } + 5 ^ { 3 }$

Perform the indicated operation. -Subtract $( 22 x + 6 )$ from $\left( - 2 x ^ { 2 } - 11 x + 6 \right)$

Express the number in scientific notation. - $0.000015717$

Perform the indicated operation. - $\left( 2 y ^ { 5 } - 7 y ^ { 4 } - 2 \right) + \left( 7 y ^ { 5 } - 9 y ^ { 4 } + 2 \right)$

Perform the indicated operation. - $5 x ^ { 3 } + 6 x ^ { 2 } + 7 x + 5 - \left( 2 x ^ { 3 } - 4 x ^ { 2 } - 9 x + 2 \right)$

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

Use the product rule to simplify the expression. Write the result using exponents. - $2 ^ { 5 } \cdot 2 ^ { 4 }$

Evaluate the expression with the given replacement values. - $4 x ^ { 2 } ; x = 6$

Simplify by combining like terms. - $5 x ^ { 2 } + 3 x y - 9 x ^ { 2 } + 14 + 2 x y$

Find the quotient using long division. - $\frac { x ^ { 2 } - 9 } { x + 3 }$

Evaluate the expression. - $3^3$

Use the product rule to simplify the expression. Write the result using exponents. - $\left( 8 p ^ { 9 } \right) \left( - 7 p ^ { 8 } \right)$

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 quotient using long division. - 6m3+25m2−21m+20m+5\frac { 6 m ^ { 3 } + 25 m ^ { 2 } - 21 m + 20 } { m + 5 }m+56m3+25m2−21m+20​

Use the power rule and the power of a product or quotient rule to simplify the expression. - (3a3b)2\left( 3 a ^ { 3 } b \right) ^ { 2 }(3a3b)2

Simplify. -If P(x)=−9x2−4xP ( x ) = - 9 x ^ { 2 } - 4 xP(x)=−9x2−4x , find P(−3)P ( - 3 )P(−3) .

Multiply using the FOIL method. - (x+10y)(x+9y)( x + 10 y ) ( x + 9 y )(x+10y)(x+9y)

Simplify the expression. Write the result using positive exponents only. - p6p−8\frac { p ^ { 6 } } { p ^ { - 8 } }p−8p6​

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - 23q2r2+rs3+14q2s23 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 14 q ^ { 2 } s23q2r2+rs3+14q2s

Simplify the expression. - 52+535 ^ { 2 } + 5 ^ { 3 }52+53

Perform the indicated operation. -Subtract (22x+6)( 22 x + 6 )(22x+6) from (−2x2−11x+6)\left( - 2 x ^ { 2 } - 11 x + 6 \right)(−2x2−11x+6)

Express the number in scientific notation. - 0.0000157170.0000157170.000015717

Perform the indicated operation. - (2y5−7y4−2)+(7y5−9y4+2)\left( 2 y ^ { 5 } - 7 y ^ { 4 } - 2 \right) + \left( 7 y ^ { 5 } - 9 y ^ { 4 } + 2 \right)(2y5−7y4−2)+(7y5−9y4+2)

Perform the indicated operation. - 5x3+6x2+7x+5−(2x3−4x2−9x+2)5 x ^ { 3 } + 6 x ^ { 2 } + 7 x + 5 - \left( 2 x ^ { 3 } - 4 x ^ { 2 } - 9 x + 2 \right)5x3+6x2+7x+5−(2x3−4x2−9x+2)

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

Use the product rule to simplify the expression. Write the result using exponents. - 25⋅242 ^ { 5 } \cdot 2 ^ { 4 }25⋅24

Evaluate the expression with the given replacement values. - 4x2;x=64 x ^ { 2 } ; x = 64x2;x=6

Complete the table for the polynomial and answer the question. - 9xy2−7x6y6z+2x3y−29 x y^{2}-7 x^{6} y^{6} z+2 x^{3} y-29xy2−7x6y6z+2x3y−2 What is the degree of the polynomial? \text { What is the degree of the polynomial? } What is the degree of the polynomial?

Simplify by combining like terms. - 5x2+3xy−9x2+14+2xy5 x ^ { 2 } + 3 x y - 9 x ^ { 2 } + 14 + 2 x y5x2+3xy−9x2+14+2xy

Find the quotient using long division. - x2−9x+3\frac { x ^ { 2 } - 9 } { x + 3 }x+3x2−9​

Solve. -The rectangle has width 7x37 x ^ { 3 }7x3 feet and length 8x48 x ^ { 4 }8x4 feet. Find its area as an expression in xxx . ((( Area === length ⋅\cdot⋅ width )))

Evaluate the expression. - 333^333

Use the product rule to simplify the expression. Write the result using exponents. - (8p9)(−7p8)\left( 8 p ^ { 9 } \right) \left( - 7 p ^ { 8 } \right)(8p9)(−7p8)