Question 1

Multiply.
-$\left( \frac { 2 } { 3 } m + 2 \right) \left( \frac { 4 } { 3 } m + 2 \right)$

Accepted Answer

A)  $\frac { 4 } { 3 } m ^ { 2 } + 4 m + 4$ 
B)  $\frac { 8 } { 9 } m ^ { 2 } + 4 m + 4$ 
C)  $\frac { 8 } { 3 } m ^ { 2 } + 4 m + 4$ 
D)  $\frac { 8 } { 3 } m ^ { 2 } + 4 m + 8$ 
A)  $\frac { 4 } { 3 } m ^ { 2 } + 4 m + 4$ 
B)  $\frac { 8 } { 9 } m ^ { 2 } + 4 m + 4$ 
C)  $\frac { 8 } { 3 } m ^ { 2 } + 4 m + 4$ 
D)  $\frac { 8 } { 3 } m ^ { 2 } + 4 m + 8$ B

Question 2

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$- 20 y z + 6 z ^ { 2 }$

Accepted Answer

A) not polynomial, first term contains 2 different variables y and z 
B) monomial 
C) trinomial 
D) binomial 
A) not polynomial, first term contains 2 different variables y and z 
B) monomial 
C) trinomial 
D) binomial D

Question 3

Multiply the polynomials.
-$( x + 12 ) \left( x ^ { 3 } + 6 x - 2 \right)$

Accepted Answer

A)  $x ^ { 3 } + 18 x ^ { 2 } + 70 x - 24$ 
B)  $x ^ { 4 } + 6 x ^ { 2 } - 2 x + 12$ 
C)  $x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } + 74 x + 24$ 
D)  $x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } + 70 x - 24$ 
A)  $x ^ { 3 } + 18 x ^ { 2 } + 70 x - 24$ 
B)  $x ^ { 4 } + 6 x ^ { 2 } - 2 x + 12$ 
C)  $x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } + 74 x + 24$ 
D)  $x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } + 70 x - 24$ D

Question 4

Find an expression for the perimeter of the figure.
-

Accepted Answer

A)  $2 x ^ { 2 } + 14 x + 36$ 
B)  $x ^ { 2 } + 12 x + 42$ 
C)  $2 x ^ { 2 } + 12 x + 42$ 
D)  $2 x ^ { 2 } + 14 x + 42$ 
A)  $2 x ^ { 2 } + 14 x + 36$ 
B)  $x ^ { 2 } + 12 x + 42$ 
C)  $2 x ^ { 2 } + 12 x + 42$ 
D)  $2 x ^ { 2 } + 14 x + 42$

Question 5

Multiply. Assume that all variables represent natural numbers.
-$12 x ^ { n } \left( - 3 x ^ { 3 n } + 3 x ^ { n } + \frac { 1 } { 9 } x \right)$

Accepted Answer

A)  $- 36 x ^ { 4 n } + 36 x ^ { 2 n } + \frac { 4 } { 3 } x ^ { n }$ 
B)  $- 36 x ^ { 4 n } - 36 x ^ { 2 n } - \frac { 4 } { 3 } x ^ { n + 1 }$ 
C)  $- 36 x ^ { 4 n } + 36 x ^ { n } + \frac { 4 } { 3 } x ^ { n + 1 }$ 
D)  $- 36 x ^ { 4 n } + 36 x ^ { 2 n } + \frac { 4 } { 3 } x ^ { n + 1 }$ 
A)  $- 36 x ^ { 4 n } + 36 x ^ { 2 n } + \frac { 4 } { 3 } x ^ { n }$ 
B)  $- 36 x ^ { 4 n } - 36 x ^ { 2 n } - \frac { 4 } { 3 } x ^ { n + 1 }$ 
C)  $- 36 x ^ { 4 n } + 36 x ^ { n } + \frac { 4 } { 3 } x ^ { n + 1 }$ 
D)  $- 36 x ^ { 4 n } + 36 x ^ { 2 n } + \frac { 4 } { 3 } x ^ { n + 1 }$

Question 6

Multiply.
-$\frac { 5 } { 9 } x w^ { 8 } \left( 8 x ^ { 2 } w ^ { 9 } + 3 x ^ { 3 } w ^ { 7 } - \frac { 7 } { 6 } \right)$

Accepted Answer

A)  $\frac { 40 } { 9 } x ^ { 3 } w ^ { 9 } + \frac { 5 } { 3 } x ^ { 3 } w ^ { 7 } - \frac { 35 } { 54 }$ 
B)  $\frac { 40 } { 9 } x ^ { 3 } { w } ^{17} + \frac { 5 } { 3 } x ^ { 4 } { w } ^{15} - \frac { 35 } { 54 } xw ^ { 8 }$ 
C)  $\frac { 40 } { 9 } x ^ { 3 } w ^ { 17 } + \frac { 5 } { 3 } x ^ { 4 } w ^ { 15 } - \frac { 7 } { 6 }$ 
D)  $\frac { 40 } { 9 } x ^ { 2 } w ^ { 17 } + \frac { 5 } { 3 } x ^ { 3 } w ^ { 15 } - \frac { 35 } { 54 } x w ^ { 8 }$ 
A)  $\frac { 40 } { 9 } x ^ { 3 } w ^ { 9 } + \frac { 5 } { 3 } x ^ { 3 } w ^ { 7 } - \frac { 35 } { 54 }$ 
B)  $\frac { 40 } { 9 } x ^ { 3 } { w } ^{17} + \frac { 5 } { 3 } x ^ { 4 } { w } ^{15} - \frac { 35 } { 54 } xw ^ { 8 }$ 
C)  $\frac { 40 } { 9 } x ^ { 3 } w ^ { 17 } + \frac { 5 } { 3 } x ^ { 4 } w ^ { 15 } - \frac { 7 } { 6 }$ 
D)  $\frac { 40 } { 9 } x ^ { 2 } w ^ { 17 } + \frac { 5 } { 3 } x ^ { 3 } w ^ { 15 } - \frac { 35 } { 54 } x w ^ { 8 }$

Question 7

Multiply.
-$10 x ( 9 x - 4 )$

Accepted Answer

A)  $90 x ^ { 2 } - 40 x$ 
B)  $9 x ^ { 2 } - 40 x$ 
C)  $90 x ^ { 2 } - 4 x$ 
D)  $50 x ^ { 2 }$ 
A)  $90 x ^ { 2 } - 40 x$ 
B)  $9 x ^ { 2 } - 40 x$ 
C)  $90 x ^ { 2 } - 4 x$ 
D)  $50 x ^ { 2 }$

Question 8

Simplify.
-( $\left( 4 x ^ { 2 } + 7 x + 7 \right) - \left( - 10 x ^ { 2 } + 1 \right)$

Accepted Answer

A)  $14 x ^ { 2 } + 7 x + 6$ 
B)  $14 x ^ { 2 } + 6 x + 7$ 
C)  $- 6 x ^ { 2 } + 6 x + 7$ 
D)  $- 6 x ^ { 2 } + 7 x + 6$ 
A)  $14 x ^ { 2 } + 7 x + 6$ 
B)  $14 x ^ { 2 } + 6 x + 7$ 
C)  $- 6 x ^ { 2 } + 6 x + 7$ 
D)  $- 6 x ^ { 2 } + 7 x + 6$

Question 9

Simplify.
-$\left( x ^ { 2 } + 4 x - 8 \right) + ( 3 x - 6 )$

Accepted Answer

A)  $3 x ^ { 2 } + 4 x - 14$ 
B)  $3 x ^ { 2 } + 7 x - 14$ 
C)  $x ^ { 2 } + 7 x - 14$ 
D)  $- 7 x ^ { 2 }$ 
A)  $3 x ^ { 2 } + 4 x - 14$ 
B)  $3 x ^ { 2 } + 7 x - 14$ 
C)  $x ^ { 2 } + 7 x - 14$ 
D)  $- 7 x ^ { 2 }$

Question 10

Give the degree of the polynomial and identify its leading coefficient.
-$21 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Accepted Answer

A) degree: 6; leading coefficient: 21 
B) degree: 5; leading coefficient: 10 
C) degree: 6; leading coefficient: -1 
D) degree: 6; leading coefficient: 2 
A) degree: 6; leading coefficient: 21 
B) degree: 5; leading coefficient: 10 
C) degree: 6; leading coefficient: -1 
D) degree: 6; leading coefficient: 2

Question 11

Determine the x-intercepts of the graph of the quadratic function. Then match the function with its graph.
-$y = x ^ { 2 } + 9 x + 20$

Accepted Answer

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

Question 12

Simplify.
-$( 12 y + 9 ) + \left( 11 y ^ { 2 } - 6 y + 9 \right)$

Accepted Answer

A)  $11 y ^ { 2 } + 18 y - 18$ 
B)  $29 y ^ { 6 }$ 
C)  $11 y ^ { 2 } - 6 y + 18$ 
D)  $11 y ^ { 2 } + 6 y + 18$ 
A)  $11 y ^ { 2 } + 18 y - 18$ 
B)  $29 y ^ { 6 }$ 
C)  $11 y ^ { 2 } - 6 y + 18$ 
D)  $11 y ^ { 2 } + 6 y + 18$

Question 13

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$9 s ^ { 4 } - 7 s - 7$

Accepted Answer

A) monomial 
B) trinomial 
C) not polynomial, no variable in last term 
D) binomial 
A) monomial 
B) trinomial 
C) not polynomial, no variable in last term 
D) binomial

Question 14

Evaluate the polynomial function at the given value.
-Find P(4)if P(x)= $x ^ { 2 } + 2 x + 4$

Accepted Answer

A) 16 
B) 24 
C) 22 
D) 28 
A) 16 
B) 24 
C) 22 
D) 28

Question 15

Give the degree of the polynomial and identify its leading coefficient.
-$- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12$

Accepted Answer

A) degree: 3; leading coefficient: 18 
B) degree: 5; leading coefficient: -9 
C) degree: 3; leading coefficient: -9 
D) degree: 5; leading coefficient: 18 
A) degree: 3; leading coefficient: 18 
B) degree: 5; leading coefficient: -9 
C) degree: 3; leading coefficient: -9 
D) degree: 5; leading coefficient: 18

Question 16

Determine which of the graphs is the graph of the equation.
-$f ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 3$

Accepted Answer

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

Question 17

Simplify.
-$\left( 3 w ^ { 2 } - 6 w \right) - \left[ \left( w ^ { 2 } + 5 w \right) - \left( 5 w ^ { 2 } - 2 w \right) \right]$

Accepted Answer

A)  $- 3 w ^ { 2 } - 9 w$ 
B)  $7 w ^ { 2 } - 9 w$ 
C)  $- 3 w ^ { 2 } - 13 w$ 
D)  $7 w ^ { 2 } - 13 w$ 
A)  $- 3 w ^ { 2 } - 9 w$ 
B)  $7 w ^ { 2 } - 9 w$ 
C)  $- 3 w ^ { 2 } - 13 w$ 
D)  $7 w ^ { 2 } - 13 w$

Question 18

Simplify.
-$\left( 28 y ^ { 2 } + 4 \right) - \left( - 11 y ^ { 4 } - 14 y ^ { 2 } + 4 \right)$

Accepted Answer

A)  $11 y ^ { 4 } + 42 y ^ { 2 } - 8$ 
B)  $- 11 y ^ { 4 } + 14 y ^ { 2 } + 8$ 
C)  $53 y ^ { 6 }$ 
D)  $11 y ^ { 4 } + 42 y ^ { 2 }$ 
A)  $11 y ^ { 4 } + 42 y ^ { 2 } - 8$ 
B)  $- 11 y ^ { 4 } + 14 y ^ { 2 } + 8$ 
C)  $53 y ^ { 6 }$ 
D)  $11 y ^ { 4 } + 42 y ^ { 2 }$

Question 19

Multiply.
-(-4x + 5)(-4x + 7)

Accepted Answer

A)  $- 8 x ^ { 2 } - 48 x - 48$ 
B)  $16 x ^ { 2 } - 48 x + 35$ 
C)  $16 x ^ { 2 } - 48 x - 48$ 
D)  $- 8 x ^ { 2 } - 48 x + 35$ 
A)  $- 8 x ^ { 2 } - 48 x - 48$ 
B)  $16 x ^ { 2 } - 48 x + 35$ 
C)  $16 x ^ { 2 } - 48 x - 48$ 
D)  $- 8 x ^ { 2 } - 48 x + 35$

Question 20

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$5 y ^ { 4 } + 5 x ^ { 2 } + 6 x + 19 x ^ { 3 }$

Accepted Answer

A)  $19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } , \text { degree } 10$ 
B)  $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 10$ 
C)  $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 4$ 
D)  $$19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } \text {, degree } 4$$ 
A)  $19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } , \text { degree } 10$ 
B)  $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 10$ 
C)  $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 4$ 
D)  $$19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } \text {, degree } 4$$

Multiply. - $\left( \frac { 2 } { 3 } m + 2 \right) \left( \frac { 4 } { 3 } m + 2 \right)$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $- 20 y z + 6 z ^ { 2 }$

Multiply the polynomials. - $( x + 12 ) \left( x ^ { 3 } + 6 x - 2 \right)$

Find an expression for the perimeter of the figure. -

Multiply. Assume that all variables represent natural numbers. - $12 x ^ { n } \left( - 3 x ^ { 3 n } + 3 x ^ { n } + \frac { 1 } { 9 } x \right)$

Multiply. - $\frac { 5 } { 9 } x w^ { 8 } \left( 8 x ^ { 2 } w ^ { 9 } + 3 x ^ { 3 } w ^ { 7 } - \frac { 7 } { 6 } \right)$

Multiply. - $10 x ( 9 x - 4 )$

Simplify. -( $\left( 4 x ^ { 2 } + 7 x + 7 \right) - \left( - 10 x ^ { 2 } + 1 \right)$

Simplify. - $\left( x ^ { 2 } + 4 x - 8 \right) + ( 3 x - 6 )$

Give the degree of the polynomial and identify its leading coefficient. - $21 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Determine the x-intercepts of the graph of the quadratic function. Then match the function with its graph. - $y = x ^ { 2 } + 9 x + 20$

Simplify. - $( 12 y + 9 ) + \left( 11 y ^ { 2 } - 6 y + 9 \right)$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $9 s ^ { 4 } - 7 s - 7$

Evaluate the polynomial function at the given value. -Find P(4)if P(x)= $x ^ { 2 } + 2 x + 4$

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12$

Determine which of the graphs is the graph of the equation. - $f ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 3$

Simplify. - $\left( 3 w ^ { 2 } - 6 w \right) - \left[ \left( w ^ { 2 } + 5 w \right) - \left( 5 w ^ { 2 } - 2 w \right) \right]$

Simplify. - $\left( 28 y ^ { 2 } + 4 \right) - \left( - 11 y ^ { 4 } - 14 y ^ { 2 } + 4 \right)$

Multiply. -(-4x + 5)(-4x + 7)

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $5 y ^ { 4 } + 5 x ^ { 2 } + 6 x + 19 x ^ { 3 }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 5: Polynomials and Polynomial Functions

Multiply. - (23m+2)(43m+2)\left( \frac { 2 } { 3 } m + 2 \right) \left( \frac { 4 } { 3 } m + 2 \right)(32​m+2)(34​m+2)

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - −20yz+6z2- 20 y z + 6 z ^ { 2 }−20yz+6z2

Multiply the polynomials. - (x+12)(x3+6x−2)( x + 12 ) \left( x ^ { 3 } + 6 x - 2 \right)(x+12)(x3+6x−2)

Find an expression for the perimeter of the figure. -

Multiply. Assume that all variables represent natural numbers. - 12xn(−3x3n+3xn+19x)12 x ^ { n } \left( - 3 x ^ { 3 n } + 3 x ^ { n } + \frac { 1 } { 9 } x \right)12xn(−3x3n+3xn+91​x)

Multiply. - 59xw8(8x2w9+3x3w7−76)\frac { 5 } { 9 } x w^ { 8 } \left( 8 x ^ { 2 } w ^ { 9 } + 3 x ^ { 3 } w ^ { 7 } - \frac { 7 } { 6 } \right)95​xw8(8x2w9+3x3w7−67​)

Multiply. - 10x(9x−4)10 x ( 9 x - 4 )10x(9x−4)

Simplify. -( (4x2+7x+7)−(−10x2+1)\left( 4 x ^ { 2 } + 7 x + 7 \right) - \left( - 10 x ^ { 2 } + 1 \right)(4x2+7x+7)−(−10x2+1)

Simplify. - (x2+4x−8)+(3x−6)\left( x ^ { 2 } + 4 x - 8 \right) + ( 3 x - 6 )(x2+4x−8)+(3x−6)

Give the degree of the polynomial and identify its leading coefficient. - 21xyz+18x2z−10y2z3+2xy−x2y2z221 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }21xyz+18x2z−10y2z3+2xy−x2y2z2

Determine the x-intercepts of the graph of the quadratic function. Then match the function with its graph. - y=x2+9x+20y = x ^ { 2 } + 9 x + 20y=x2+9x+20

Simplify. - (12y+9)+(11y2−6y+9)( 12 y + 9 ) + \left( 11 y ^ { 2 } - 6 y + 9 \right)(12y+9)+(11y2−6y+9)

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - 9s4−7s−79 s ^ { 4 } - 7 s - 79s4−7s−7

Evaluate the polynomial function at the given value. -Find P(4)if P(x)= x2+2x+4x ^ { 2 } + 2 x + 4x2+2x+4

Give the degree of the polynomial and identify its leading coefficient. - −9x3−8x4+18x5+12- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12−9x3−8x4+18x5+12

Determine which of the graphs is the graph of the equation. - f(x)=−6x3−3x2+3x−3f ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 3f(x)=−6x3−3x2+3x−3

Simplify. - (3w2−6w)−[(w2+5w)−(5w2−2w)]\left( 3 w ^ { 2 } - 6 w \right) - \left[ \left( w ^ { 2 } + 5 w \right) - \left( 5 w ^ { 2 } - 2 w \right) \right](3w2−6w)−[(w2+5w)−(5w2−2w)]

Simplify. - (28y2+4)−(−11y4−14y2+4)\left( 28 y ^ { 2 } + 4 \right) - \left( - 11 y ^ { 4 } - 14 y ^ { 2 } + 4 \right)(28y2+4)−(−11y4−14y2+4)