Question 1

Multiply.
-$$( x + 11 ) ( x - 11 )$$

Accepted Answer

A)  $x ^ { 2 } - 121$ 
B)  $x ^ { 2 } - 22 x - 121$ 
C)  $x ^ { 2 } - 22$ 
D)  $x ^ { 2 } + 22 x - 121$ 
A)  $x ^ { 2 } - 121$ 
B)  $x ^ { 2 } - 22 x - 121$ 
C)  $x ^ { 2 } - 22$ 
D)  $x ^ { 2 } + 22 x - 121$

Question 2

Perform the indicated operations and simplify.
-$$\left( - 6 x ^ { 2 } y - x y \right) + \left( 8 x ^ { 2 } y + 3 x y \right)$$

Accepted Answer

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

Question 3

Solve the equation.
-$$3 ( x - 2 ) ( x - 4 ) = 0$$

Accepted Answer

A)  $\{ - 2 , - 4 \}$ 
B)  $\{ 3,2,4 \}$ 
C)  $\{ 2,4 \}$ 
D)  $\{ 0,2,4 \}$ 
A)  $\{ - 2 , - 4 \}$ 
B)  $\{ 3,2,4 \}$ 
C)  $\{ 2,4 \}$ 
D)  $\{ 0,2,4 \}$

Question 4

Find the GCF of the list of monomials.
-$4 \mathrm { y } , 8 \mathrm { y }$

Accepted Answer

A)  $y$ 
B)  $2 \mathrm { y }$ 
C)  $4 \mathrm { y }$ 
D)  8 
A)  $y$ 
B)  $2 \mathrm { y }$ 
C)  $4 \mathrm { y }$ 
D)  8

Question 5

Factor completely.
-$$n ^ { 3 } - \frac { 1 } { 64 }$$

Accepted Answer

A)  $\left( n - \frac { 1 } { 4 } \right) \left( n ^ { 2 } + \frac { 1 } { 4 } n + \frac { 1 } { 16 } \right)$ 
B)  $\left( n + \frac { 1 } { 16 } \right) \left( n ^ { 2 } - \frac { 1 } { 4 } n + \frac { 1 } { 4 } \right)$ 
C)  $\left( n - \frac { 1 } { 16 } \right) \left( n ^ { 2 } + \frac { 1 } { 4 } n + \frac { 1 } { 4 } \right)$ 
D)  $\left( n + \frac { 1 } { 4 } \right) \left( n ^ { 2 } - \frac { 1 } { 4 } n + \frac { 1 } { 16 } \right)$ 
A)  $\left( n - \frac { 1 } { 4 } \right) \left( n ^ { 2 } + \frac { 1 } { 4 } n + \frac { 1 } { 16 } \right)$ 
B)  $\left( n + \frac { 1 } { 16 } \right) \left( n ^ { 2 } - \frac { 1 } { 4 } n + \frac { 1 } { 4 } \right)$ 
C)  $\left( n - \frac { 1 } { 16 } \right) \left( n ^ { 2 } + \frac { 1 } { 4 } n + \frac { 1 } { 4 } \right)$ 
D)  $\left( n + \frac { 1 } { 4 } \right) \left( n ^ { 2 } - \frac { 1 } { 4 } n + \frac { 1 } { 16 } \right)$

Question 6

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-$- 8 x y ^ { 2 }$

Accepted Answer

A)  binomial of degree 3 
B)  trinomial of degree 3 
C)  monomial of degree 2 
D)  monomial of degree 3 
A)  binomial of degree 3 
B)  trinomial of degree 3 
C)  monomial of degree 2 
D)  monomial of degree 3

Question 7

Multiply.
-$$( 9 x - 8 y ) ^ { 2 }$$

Accepted Answer

A)  $81 x ^ { 2 } - 144 x y + 64 y ^ { 2 }$ 
B)  $81 x ^ { 2 } + 64 y ^ { 2 }$ 
C)  $9 x ^ { 2 } + 64 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 144 x y + 64 y ^ { 2 }$ 
A)  $81 x ^ { 2 } - 144 x y + 64 y ^ { 2 }$ 
B)  $81 x ^ { 2 } + 64 y ^ { 2 }$ 
C)  $9 x ^ { 2 } + 64 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 144 x y + 64 y ^ { 2 }$

Question 8

Factor the trinomial.
-$$9 x ^ { 2 } + 13 x - 10$$

Accepted Answer

A)  $( 9 x + 5 ) ( x - 2 )$ 
B)  $( 9 x - 5 ) ( x + 2 )$ 
C)  $( 9 x + 2 ) ( x - 5 )$ 
D)  prime polynomial 
A)  $( 9 x + 5 ) ( x - 2 )$ 
B)  $( 9 x - 5 ) ( x + 2 )$ 
C)  $( 9 x + 2 ) ( x - 5 )$ 
D)  prime polynomial

Question 9

Multiply.
-$$( 7 x y + 8 z ) ( 7 x y - 8 z )$$

Accepted Answer

A)  $49 x ^ { 2 } y ^ { 2 } - 112 x y z - 64 z ^ { 2 }$ 
B)  $x ^ { 2 } y ^ { 2 } - 64 z ^ { 2 }$ 
C)  $49 x ^ { 2 } y ^ { 2 } + 112 x y z - 64 z ^ { 2 }$ 
D)  $49 x ^ { 2 } y ^ { 2 } - 64 z ^ { 2 }$ 
A)  $49 x ^ { 2 } y ^ { 2 } - 112 x y z - 64 z ^ { 2 }$ 
B)  $x ^ { 2 } y ^ { 2 } - 64 z ^ { 2 }$ 
C)  $49 x ^ { 2 } y ^ { 2 } + 112 x y z - 64 z ^ { 2 }$ 
D)  $49 x ^ { 2 } y ^ { 2 } - 64 z ^ { 2 }$

Question 10

Factor out the greatest common factor.
-$42 x ^ { 4 } + 30 x ^ { 2 }$

Accepted Answer

A)  $6 x ^ { 2 } ( 7 x + 5 )$ 
B)  $6 \times \left( 7 x ^ { 3 } + 5 \right)$ 
C)  $6 x ^ { 2 } \left( 7 x ^ { 2 } + 5 \right)$ 
D)  $x ^ { 2 } \left( 42 x ^ { 2 } + 30 \right)$ 
A)  $6 x ^ { 2 } ( 7 x + 5 )$ 
B)  $6 \times \left( 7 x ^ { 3 } + 5 \right)$ 
C)  $6 x ^ { 2 } \left( 7 x ^ { 2 } + 5 \right)$ 
D)  $x ^ { 2 } \left( 42 x ^ { 2 } + 30 \right)$

Question 11

Factor the polynomial.
-$32 a ^ { 2 } b c + 20 a b + 32 b ^ { 2 } c + 4 a b c$

Accepted Answer

A)  $4 a \left( 8 a b c + 5 b + 8 b ^ { 2 } c + b c \right)$ 
B)  $4 b \left( 8 a ^ { 2 } c + 5 a + 8 b c + a c \right)$ 
C)  $4 a b ( 8 a c + 5 + 8 b c + c )$ 
D)  $4 b \left( 8 a ^ { 2 } c + 5 a + 8 c + a c \right)$ 
A)  $4 a \left( 8 a b c + 5 b + 8 b ^ { 2 } c + b c \right)$ 
B)  $4 b \left( 8 a ^ { 2 } c + 5 a + 8 b c + a c \right)$ 
C)  $4 a b ( 8 a c + 5 + 8 b c + c )$ 
D)  $4 b \left( 8 a ^ { 2 } c + 5 a + 8 c + a c \right)$

Question 12

Factor out the greatest common factor.
-$36 x + 12 y - 12$

Accepted Answer

A)  $12 ( 3 x + y - 1 )$ 
B)  $12 x ( 3 + y )$ 
C)  $12 ( 3 x + y - 12 )$ 
D)  $12 ( 3 x + y )$ 
A)  $12 ( 3 x + y - 1 )$ 
B)  $12 x ( 3 + y )$ 
C)  $12 ( 3 x + y - 12 )$ 
D)  $12 ( 3 x + y )$

Question 13

Factor. Assume that variables used as exponents represent positive integers.
-$$7 x ^ { 2 n } + 5 x ^ { n } - 18$$

Accepted Answer

A)  $\left( \mathrm { x } ^ { \mathrm { n } } - 9 \right) \left( 7 \mathrm { x } ^ { \mathrm { n } } + 2 \right)$ 
B)  $\left( x ^ { n } + 2 \right) \left( 7 x ^ { n } - 9 \right)$ 
C)  $\left( x ^ { n } - 2 \right) \left( 7 x ^ { n } + 9 \right)$ 
D)  prime polynomial 
A)  $\left( \mathrm { x } ^ { \mathrm { n } } - 9 \right) \left( 7 \mathrm { x } ^ { \mathrm { n } } + 2 \right)$ 
B)  $\left( x ^ { n } + 2 \right) \left( 7 x ^ { n } - 9 \right)$ 
C)  $\left( x ^ { n } - 2 \right) \left( 7 x ^ { n } + 9 \right)$ 
D)  prime polynomial

Question 14

Match the polynomial function with its graph.
-$$f ( x ) = ( x - 5 ) ( x - 2 )$$

Accepted Answer

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

Question 15

Simplify the polynomial by combining like terms.
-$$4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x$$

Accepted Answer

A)  $12 x ^ { 3 } + 13 x$ 
B)  $25 \mathrm { x } ^ { 3 }$ 
C)  $4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x$ 
D)  $25 x$ 
A)  $12 x ^ { 3 } + 13 x$ 
B)  $25 \mathrm { x } ^ { 3 }$ 
C)  $4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x$ 
D)  $25 x$

Question 16

Find the degree of the term.
$- 5 x y ^ { 7 }$

Accepted Answer

A)   -5 
B)  8 
C)  7 
D)  no degree 
A)   -5 
B)  8 
C)  7 
D)  no degree

Question 17

Factor completely.
-$$x ^ { 4 } - 1296$$

Accepted Answer

A)  $( x + 6 ) ^ { 2 } ( x - 6 ) ^ { 2 }$ 
B)  $\left( x ^ { 2 } + 36 \right) ( x - 6 ) ^ { 2 }$ 
C)  $\left( x ^ { 2 } + 36 \right) ( x + 6 ) ( x - 6 )$ 
D)  $\left( x ^ { 2 } + 36 \right) \left( x ^ { 2 } - 36 \right)$ 
A)  $( x + 6 ) ^ { 2 } ( x - 6 ) ^ { 2 }$ 
B)  $\left( x ^ { 2 } + 36 \right) ( x - 6 ) ^ { 2 }$ 
C)  $\left( x ^ { 2 } + 36 \right) ( x + 6 ) ( x - 6 )$ 
D)  $\left( x ^ { 2 } + 36 \right) \left( x ^ { 2 } - 36 \right)$

Question 18

Perform the indicated operations and simplify.
-$$\begin{array} { r } 
8 x ^ { 7 } + 4 x ^ { 6 } + 4 x \
+ \left( 2 x ^ { 7 } + 4 x ^ { 6 } + 2 x \right) \
\hline
\end{array}$$

Accepted Answer

A)  $10 x + 8 x ^ { 7 } + 6 x ^ { 6 }$ 
B)  $24 \mathrm { x } ^ { 14 }$ 
C)  $6 x ^ { 7 } + 12 x ^ { 6 } + 6 x$ 
D)  $10 x ^ { 7 } + 8 x ^ { 6 } + 6 x$ 
A)  $10 x + 8 x ^ { 7 } + 6 x ^ { 6 }$ 
B)  $24 \mathrm { x } ^ { 14 }$ 
C)  $6 x ^ { 7 } + 12 x ^ { 6 } + 6 x$ 
D)  $10 x ^ { 7 } + 8 x ^ { 6 } + 6 x$

Question 19

Factor the polynomial completely.
-$$x ^ { 2 } + 6 x - 16$$

Accepted Answer

A)  $( x - 8 ) ( x - 2 )$ 
B)  $( x - 8 ) ( x + 1 )$ 
C)  prime polynomial 
D)  $( x + 8 ) ( x - 2 )$ 
A)  $( x - 8 ) ( x - 2 )$ 
B)  $( x - 8 ) ( x + 1 )$ 
C)  prime polynomial 
D)  $( x + 8 ) ( x - 2 )$

Question 20

Factor out the greatest common factor.
-$$60 x + 20$$

Accepted Answer

A)  $4 ( 15 x + 5 )$ 
B)  $20 ( 3 x )$ 
C)  $5 ( 12 x + 4 )$ 
D)  $20 ( 3 x + 1 )$ 
A)  $4 ( 15 x + 5 )$ 
B)  $20 ( 3 x )$ 
C)  $5 ( 12 x + 4 )$ 
D)  $20 ( 3 x + 1 )$

Multiply. - $( x + 11 ) ( x - 11 )$

Perform the indicated operations and simplify. - $\left( - 6 x ^ { 2 } y - x y \right) + \left( 8 x ^ { 2 } y + 3 x y \right)$

Solve the equation. - $3 ( x - 2 ) ( x - 4 ) = 0$

Find the GCF of the list of monomials. - $4 \mathrm { y } , 8 \mathrm { y }$

Factor completely. - $n ^ { 3 } - \frac { 1 } { 64 }$

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - $- 8 x y ^ { 2 }$

Multiply. - $( 9 x - 8 y ) ^ { 2 }$

Factor the trinomial. - $9 x ^ { 2 } + 13 x - 10$

Multiply. - $( 7 x y + 8 z ) ( 7 x y - 8 z )$

Factor out the greatest common factor. - $42 x ^ { 4 } + 30 x ^ { 2 }$

Factor the polynomial. - $32 a ^ { 2 } b c + 20 a b + 32 b ^ { 2 } c + 4 a b c$

Factor out the greatest common factor. - $36 x + 12 y - 12$

Factor. Assume that variables used as exponents represent positive integers. - $7 x ^ { 2 n } + 5 x ^ { n } - 18$

Match the polynomial function with its graph. - $f ( x ) = ( x - 5 ) ( x - 2 )$

Simplify the polynomial by combining like terms. - $4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x$

Find the degree of the term. $- 5 x y ^ { 7 }$

Factor completely. - $x ^ { 4 } - 1296$

Perform the indicated operations and simplify. - 8+4+4x + 2+4+2x

Factor the polynomial completely. - $x ^ { 2 } + 6 x - 16$

Factor out the greatest common factor. - $60 x + 20$

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. - (x+11)(x−11)( x + 11 ) ( x - 11 )(x+11)(x−11)

Perform the indicated operations and simplify. - (−6x2y−xy)+(8x2y+3xy)\left( - 6 x ^ { 2 } y - x y \right) + \left( 8 x ^ { 2 } y + 3 x y \right)(−6x2y−xy)+(8x2y+3xy)

Solve the equation. - 3(x−2)(x−4)=03 ( x - 2 ) ( x - 4 ) = 03(x−2)(x−4)=0

Find the GCF of the list of monomials. - 4y,8y4 \mathrm { y } , 8 \mathrm { y }4y,8y

Factor completely. - n3−164n ^ { 3 } - \frac { 1 } { 64 }n3−641​

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - −8xy2- 8 x y ^ { 2 }−8xy2

Multiply. - (9x−8y)2( 9 x - 8 y ) ^ { 2 }(9x−8y)2

Factor the trinomial. - 9x2+13x−109 x ^ { 2 } + 13 x - 109x2+13x−10

Multiply. - (7xy+8z)(7xy−8z)( 7 x y + 8 z ) ( 7 x y - 8 z )(7xy+8z)(7xy−8z)

Factor out the greatest common factor. - 42x4+30x242 x ^ { 4 } + 30 x ^ { 2 }42x4+30x2

Factor the polynomial. - 32a2bc+20ab+32b2c+4abc32 a ^ { 2 } b c + 20 a b + 32 b ^ { 2 } c + 4 a b c32a2bc+20ab+32b2c+4abc

Factor out the greatest common factor. - 36x+12y−1236 x + 12 y - 1236x+12y−12

Factor. Assume that variables used as exponents represent positive integers. - 7x2n+5xn−187 x ^ { 2 n } + 5 x ^ { n } - 187x2n+5xn−18

Match the polynomial function with its graph. - f(x)=(x−5)(x−2)f ( x ) = ( x - 5 ) ( x - 2 )f(x)=(x−5)(x−2)

Simplify the polynomial by combining like terms. - 4x+4x3+8x3+9x4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x4x+4x3+8x3+9x

Find the degree of the term. −5xy7- 5 x y ^ { 7 }−5xy7

Factor completely. - x4−1296x ^ { 4 } - 1296x4−1296