Question 1

Factor completely.
-$$\mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 27$$

Accepted Answer

A)  $( p q - 3 ) \left( p ^ { 2 } q ^ { 2 } + 3 p q + 9 \right)$ 
B)  $( p q - 3 ) \left( p ^ { 2 } q ^ { 2 } + 3 p q - 9 \right)$ 
C)  $( \mathrm { pq } + 3 ) \left( \mathrm { p } ^ { 2 } \mathrm { q } ^ { 2 } - 3 \mathrm { pq } + 9 \right)$ 
D)  $( \mathrm { pq } + 3 ) \left( \mathrm { p } ^ { 2 } \mathrm { q } ^ { 2 } + 3 \mathrm { pq } + 9 \right)$ 
A)  $( p q - 3 ) \left( p ^ { 2 } q ^ { 2 } + 3 p q + 9 \right)$ 
B)  $( p q - 3 ) \left( p ^ { 2 } q ^ { 2 } + 3 p q - 9 \right)$ 
C)  $( \mathrm { pq } + 3 ) \left( \mathrm { p } ^ { 2 } \mathrm { q } ^ { 2 } - 3 \mathrm { pq } + 9 \right)$ 
D)  $( \mathrm { pq } + 3 ) \left( \mathrm { p } ^ { 2 } \mathrm { q } ^ { 2 } + 3 \mathrm { pq } + 9 \right)$

Question 2

Divide.
-$\frac { - 56 x ^ { 5 } - 28 x ^ { 4 } - 21 x ^ { 3 } } { - 7 x ^ { 4 } }$

Accepted Answer

A)  $8 x + 4 + \frac { 3 } { x }$ 
B)  $8 x + 4$ 
C)  $8 x - 28 x ^ { 4 } + \frac { 3 } { x }$ 
D)  $11 \mathrm { x } + 4$ 
A)  $8 x + 4 + \frac { 3 } { x }$ 
B)  $8 x + 4$ 
C)  $8 x - 28 x ^ { 4 } + \frac { 3 } { x }$ 
D)  $11 \mathrm { x } + 4$

Question 3

Evaluate the polynomial function.
-If $f ( x ) = x ^ { 2 } - 3 x$, find $f ( a + h )$.

Accepted Answer

A)  $a ^ { 2 } + a h + h ^ { 2 } - 3 a - 3 h$ 
B)  $a ^ { 2 } + 2 a h + h ^ { 2 } - 3 a - 3 h$ 
C)  $a ^ { 2 } + h ^ { 2 } - 3 a h$ 
D)  $a ^ { 2 } + h ^ { 2 } - 3 a - 3 h$ 
A)  $a ^ { 2 } + a h + h ^ { 2 } - 3 a - 3 h$ 
B)  $a ^ { 2 } + 2 a h + h ^ { 2 } - 3 a - 3 h$ 
C)  $a ^ { 2 } + h ^ { 2 } - 3 a h$ 
D)  $a ^ { 2 } + h ^ { 2 } - 3 a - 3 h$

Question 4

Multiply.
-$$\left( 2 x ^ { 2 } + 7 y \right) \left( - 5 x ^ { 2 } + 4 y \right)$$

Accepted Answer

A)  $- 10 x ^ { 4 } - 27 x ^ { 2 } y + 28 y ^ { 4 }$ 
B)  $- 10 x ^ { 4 } - 27 x ^ { 2 } y ^ { 2 } + 28 y ^ { 2 }$ 
C)  $- 10 x ^ { 2 } - 27 x y + 28 y ^ { 2 }$ 
D)  $- 10 x ^ { 4 } - 27 x ^ { 2 } y + 28 y ^ { 2 }$ 
A)  $- 10 x ^ { 4 } - 27 x ^ { 2 } y + 28 y ^ { 4 }$ 
B)  $- 10 x ^ { 4 } - 27 x ^ { 2 } y ^ { 2 } + 28 y ^ { 2 }$ 
C)  $- 10 x ^ { 2 } - 27 x y + 28 y ^ { 2 }$ 
D)  $- 10 x ^ { 4 } - 27 x ^ { 2 } y + 28 y ^ { 2 }$

Question 5

Multiply.
-$$( b - 10 ) ( b - 3 )$$

Accepted Answer

A)  $b ^ { 2 } + 13 b - 30$ 
B)  $2 b + 30$ 
C)  $b ^ { 2 } - 13 b + 30$ 
D)  $2 b ^ { 2 } - 30$ 
A)  $b ^ { 2 } + 13 b - 30$ 
B)  $2 b + 30$ 
C)  $b ^ { 2 } - 13 b + 30$ 
D)  $2 b ^ { 2 } - 30$

Question 6

10

Accepted Answer

A)  0 
B)  10 
C)  1 
D)  no degree 
A)  0 
B)  10 
C)  1 
D)  no degree

Question 7

Find the perimeter.
-

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 8 x + 31 \right)$ units 
B)  $\left( 4 x ^ { 2 } + 8 x + 20 \right)$ units 
C)  $\left( 4 x ^ { 2 } + 2 x + 31 \right)$ units 
D)  $\left( 3 x ^ { 2 } + 2 x + 20 \right)$ units 
A)  $\left( 4 x ^ { 2 } + 8 x + 31 \right)$ units 
B)  $\left( 4 x ^ { 2 } + 8 x + 20 \right)$ units 
C)  $\left( 4 x ^ { 2 } + 2 x + 31 \right)$ units 
D)  $\left( 3 x ^ { 2 } + 2 x + 20 \right)$ units

Question 8

Fill in the blank with one of the words or phrases listed below.

-The order may be used when multiplying two binomials.

Accepted Answer

A) trinomial 
B)  monomial 
C)  binomial 
D)  FOIL 
A) trinomial 
B)  monomial 
C)  binomial 
D)  FOIL

Question 9

Find the GCF of the list of monomials.
-$$x ^ { 2 } , x ^ { 3 } , x ^ { 5 }$$

Accepted Answer

A)  $x ^ { 5 }$ 
B)  $x$ 
C)  $x ^ { 2 }$ 
D)  $x ^ { 10 }$ 
A)  $x ^ { 5 }$ 
B)  $x$ 
C)  $x ^ { 2 }$ 
D)  $x ^ { 10 }$

Question 10

Multiply.
-$$( z - 8 ) ( z + 3 )$$

Accepted Answer

A)  $2 z - 24$ 
B)  $z ^ { 2 } + 5 z + 24$ 
C)  $2 z ^ { 2 } + 24$ 
D)  $z ^ { 2 } - 5 z - 24$ 
A)  $2 z - 24$ 
B)  $z ^ { 2 } + 5 z + 24$ 
C)  $2 z ^ { 2 } + 24$ 
D)  $z ^ { 2 } - 5 z - 24$

Question 11

Factor.
-$$x ^ { 2 } + 10 x + 25$$

Accepted Answer

A)  $( x + 5 ) ^ { 2 }$ 
B)  $( x - 5 ) ^ { 2 }$ 
C)  $( x + 10 ) ( x - 10 )$ 
D)  $( x + 5 ) ( x - 5 )$ 
A)  $( x + 5 ) ^ { 2 }$ 
B)  $( x - 5 ) ^ { 2 }$ 
C)  $( x + 10 ) ( x - 10 )$ 
D)  $( x + 5 ) ( x - 5 )$

Question 12

Factor. Assume that variables used as exponents represent positive integers.
-$$25 x ^ { 2 n } - 60 x ^ { n } + 36$$

Accepted Answer

A)  $\left( 5 x ^ { n } - 6 \right) ^ { 2 }$ 
B)  $\left( 25 \mathrm { x } ^ { \mathrm { n } } + 1 \right) \left( \mathrm { x } ^ { \mathrm { n } } + 36 \right)$ 
C)  $\left( 5 x ^ { n } - 6 \right) \left( 5 x ^ { n } + 6 \right)$ 
D)  $\left( 5 x ^ { n } + 6 \right) ^ { 2 }$ 
A)  $\left( 5 x ^ { n } - 6 \right) ^ { 2 }$ 
B)  $\left( 25 \mathrm { x } ^ { \mathrm { n } } + 1 \right) \left( \mathrm { x } ^ { \mathrm { n } } + 36 \right)$ 
C)  $\left( 5 x ^ { n } - 6 \right) \left( 5 x ^ { n } + 6 \right)$ 
D)  $\left( 5 x ^ { n } + 6 \right) ^ { 2 }$

Question 13

Subtract.
-$$\begin{array} { r } 
5 x ^ { 8 } + 4 x ^ { 7 } + 5 x ^ { 6 } - 6 \
- \left( 3 x ^ { 8 } + 9 x ^ { 7 } - 7 x ^ { 6 } - 2 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $2 x ^ { 8 } - 5 x ^ { 7 } + 12 x ^ { 6 } - 4$ 
B)  $8 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 4$ 
C)  $8 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
D)  $2 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
A)  $2 x ^ { 8 } - 5 x ^ { 7 } + 12 x ^ { 6 } - 4$ 
B)  $8 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 4$ 
C)  $8 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
D)  $2 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 8$

Question 14

Factor.
-$50 x ^ { 2 } + 160 x y + 128 y ^ { 2 }$

Accepted Answer

A)  $2 ( 5 x - 8 y ) ^ { 2 }$ 
B)  $2 ( 5 x + 8 y ) ( 5 x - 8 y )$ 
C)  $2 ( 5 x + 8 y ) ^ { 2 }$ 
D)  prime polynomial 
A)  $2 ( 5 x - 8 y ) ^ { 2 }$ 
B)  $2 ( 5 x + 8 y ) ( 5 x - 8 y )$ 
C)  $2 ( 5 x + 8 y ) ^ { 2 }$ 
D)  prime polynomial

Question 15

Factor the polynomial completely.
-$$x ^ { 3 } + 1000$$

Accepted Answer

A)  $( x - 1000 ) ( x + 1 ) ( x - 1 )$ 
B)  $( x + 10 ) \left( x ^ { 2 } - 10 x + 100 \right)$ 
C)  $( x - 10 ) \left( x ^ { 2 } + 10 x + 100 \right)$ 
D)  $( x + 10 ) \left( x ^ { 2 } + 100 \right)$ 
A)  $( x - 1000 ) ( x + 1 ) ( x - 1 )$ 
B)  $( x + 10 ) \left( x ^ { 2 } - 10 x + 100 \right)$ 
C)  $( x - 10 ) \left( x ^ { 2 } + 10 x + 100 \right)$ 
D)  $( x + 10 ) \left( x ^ { 2 } + 100 \right)$

Question 16

Factor.
-$3 x ^ { 2 } - 12$

Accepted Answer

A)  $3 ( x + 2 ) ^ { 2 }$ 
B)  $3 ( x + 2 ) ( x - 2 )$ 
C)  $3 ( x - 2 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $3 ( x + 2 ) ^ { 2 }$ 
B)  $3 ( x + 2 ) ( x - 2 )$ 
C)  $3 ( x - 2 ) ^ { 2 }$ 
D)  prime polynomial

Question 17

Evaluate the polynomial function.
-If $f ( x ) = x ^ { 2 } - 2 x + 9$, find $f ( a - 7 )$

Accepted Answer

A)  $a ^ { 2 } - 2 a + 72$ 
B)  $a ^ { 2 } - 16 a + 72$ 
C)  $a ^ { 2 } - 16 a + 51$ 
D)  $a ^ { 2 } - 2 a + 81$ 
A)  $a ^ { 2 } - 2 a + 72$ 
B)  $a ^ { 2 } - 16 a + 72$ 
C)  $a ^ { 2 } - 16 a + 51$ 
D)  $a ^ { 2 } - 2 a + 81$

Question 18

Subtract.
-$\left( 2.6 x ^ { 3 } - 6.2 x ^ { 2 } - 1 \right) - \left( 8.5 x ^ { 3 } - 2.4 x ^ { 2 } + 3 \right)$

Accepted Answer

A)  $11.1 x ^ { 3 } - 3.8 x ^ { 2 } - 4$ 
B)  $- 5.9 x ^ { 3 } - 3.8 x ^ { 2 } + 4$ 
C)  $- 5.9 x ^ { 3 } - 8.6 x ^ { 2 } - 4$ 
D)  $- 5.9 x ^ { 3 } - 3.8 x ^ { 2 } - 4$ 
A)  $11.1 x ^ { 3 } - 3.8 x ^ { 2 } - 4$ 
B)  $- 5.9 x ^ { 3 } - 3.8 x ^ { 2 } + 4$ 
C)  $- 5.9 x ^ { 3 } - 8.6 x ^ { 2 } - 4$ 
D)  $- 5.9 x ^ { 3 } - 3.8 x ^ { 2 } - 4$

Question 19

Factor.
-$$x ^ { 2 } - 64$$

Accepted Answer

A)  $( x + 8 ) ^ { 2 }$ 
B)  $( x - 8 ) ^ { 2 }$ 
C)  $( x + 8 ) ( x - 8 )$ 
D)  prime polynomial 
A)  $( x + 8 ) ^ { 2 }$ 
B)  $( x - 8 ) ^ { 2 }$ 
C)  $( x + 8 ) ( x - 8 )$ 
D)  prime polynomial

Question 20

Find the degree of the term.
$- 3 ^ { 5 } y ^ { 2 }$

Accepted Answer

A)  5 
B)  2 
C)  7 
D)  no degree 
A)  5 
B)  2 
C)  7 
D)  no degree

Factor completely. - $\mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 27$

Divide. - $\frac { - 56 x ^ { 5 } - 28 x ^ { 4 } - 21 x ^ { 3 } } { - 7 x ^ { 4 } }$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } - 3 x$ , find $f ( a + h )$ .

Multiply. - $\left( 2 x ^ { 2 } + 7 y \right) \left( - 5 x ^ { 2 } + 4 y \right)$

Multiply. - $( b - 10 ) ( b - 3 )$

10

Find the perimeter. -

Fill in the blank with one of the words or phrases listed below. -The order may be used when multiplying two binomials.

Find the GCF of the list of monomials. - $x ^ { 2 } , x ^ { 3 } , x ^ { 5 }$

Multiply. - $( z - 8 ) ( z + 3 )$

Factor. - $x ^ { 2 } + 10 x + 25$

Factor. Assume that variables used as exponents represent positive integers. - $25 x ^ { 2 n } - 60 x ^ { n } + 36$

Subtract. - 5+4+5-6 - 3+9-7-2

Factor. - $50 x ^ { 2 } + 160 x y + 128 y ^ { 2 }$

Factor the polynomial completely. - $x ^ { 3 } + 1000$

Factor. - $3 x ^ { 2 } - 12$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } - 2 x + 9$ , find $f ( a - 7 )$

Subtract. - $\left( 2.6 x ^ { 3 } - 6.2 x ^ { 2 } - 1 \right) - \left( 8.5 x ^ { 3 } - 2.4 x ^ { 2 } + 3 \right)$

Factor. - $x ^ { 2 } - 64$

Find the degree of the term. $- 3 ^ { 5 } y ^ { 2 }$

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

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Filters

Exam 5: Polynomials and Polynomial Functions

Factor completely. - p3q3+27\mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 27p3q3+27

Divide. - −56x5−28x4−21x3−7x4\frac { - 56 x ^ { 5 } - 28 x ^ { 4 } - 21 x ^ { 3 } } { - 7 x ^ { 4 } }−7x4−56x5−28x4−21x3​

Evaluate the polynomial function. -If f(x)=x2−3xf ( x ) = x ^ { 2 } - 3 xf(x)=x2−3x , find f(a+h)f ( a + h )f(a+h) .

Multiply. - (2x2+7y)(−5x2+4y)\left( 2 x ^ { 2 } + 7 y \right) \left( - 5 x ^ { 2 } + 4 y \right)(2x2+7y)(−5x2+4y)

Multiply. - (b−10)(b−3)( b - 10 ) ( b - 3 )(b−10)(b−3)

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