Question 1

For the given pair of functions, find the requested function.
-$f(x)=5 x-3, g(x)=-7 x^{2}-16 x+9 ;(f-g)(x)$

Accepted Answer

A)  $-7 x^{2}-11 x+6$ 
B)  $7 x^{2}-11 x-12$ 
C)  $7 x^{2}+21 x-12$ 
D)  $-7 x^{2}+21 x+12$ 
A)  $-7 x^{2}-11 x+6$ 
B)  $7 x^{2}-11 x-12$ 
C)  $7 x^{2}+21 x-12$ 
D)  $-7 x^{2}+21 x+12$

Question 2

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.
-$(-\mathrm{a})^{-18}$

Accepted Answer

A)  $\frac{1}{-a^{18}}$ 
B)  $18 \mathrm{a}$ 
C)  $\frac{1}{a^{-18}}$ 
D)  $\frac{1}{a^{18}}$ 
A)  $\frac{1}{-a^{18}}$ 
B)  $18 \mathrm{a}$ 
C)  $\frac{1}{a^{-18}}$ 
D)  $\frac{1}{a^{18}}$

Question 3

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.
-$\frac{x^{-17}}{x^{-8}}$

Accepted Answer

A)  $\frac{1}{x^{25}}$ 
B)  $\frac{1}{x^{9}}$ 
C)  $x^{9}$ 
D)  $-x^{25}$ 
A)  $\frac{1}{x^{25}}$ 
B)  $\frac{1}{x^{9}}$ 
C)  $x^{9}$ 
D)  $-x^{25}$

Question 4

Explain how you can use the special product $(a+b)(a-b)$ to find the product of $34 \cdot 26$.

Accepted Answer

Answers will vary, b

Question 5

Provide an appropriate response.
-Let $f(x)=x^{2}-7$ and $g(x)=2 x+6$. Find $(f-g)(5)$.

Accepted Answer

A)  2 
B)  7 
C)  3 
D)  0 
A)  2 
B)  7 
C)  3 
D)  0

Question 6

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(x^{3}\right)^{-3}$

Accepted Answer

A)  $\frac{1}{x^{9}}$ 
B)  $x^{6}$ 
C)  $x^{9}$ 
D)  $\frac{1}{x^{6}}$ 
A)  $\frac{1}{x^{9}}$ 
B)  $x^{6}$ 
C)  $x^{9}$ 
D)  $\frac{1}{x^{6}}$

Question 7

Express the area of the figure as a polynomial in descending powers of the variable $x$.
-

Accepted Answer

A)  $x^{2}+3 x+3$ 
B)  $x^{2}+3 x+9$ 
C)  $x^{2}-6 x+9$ 
D)  $x^{2}+6 x+9$ 
A)  $x^{2}+3 x+3$ 
B)  $x^{2}+3 x+9$ 
C)  $x^{2}-6 x+9$ 
D)  $x^{2}+6 x+9$

Question 8

Express the number in standard notation.
-$3.448 \times 10^{-5}$

Accepted Answer

A)  $-344,800$ 
B)  0.00003448 
C)  0.000003448 
D)  0.0003448 
A)  $-344,800$ 
B)  0.00003448 
C)  0.000003448 
D)  0.0003448

Question 9

Decide whether the expression has been simplified correctly.
-$(a b)^{2}=a^{2} b^{2}$

Accepted Answer

A) True 
 B)False

Question 10

Find the product
-$\left(-2 x^{4} y^{4}\right)\left(-4 x^{3} y^{2}\right)$

Accepted Answer

A)  $8 x^{7} y^{6}$ 
B)  $8 x y^{6}$ 
C)  $8 x y^{7}$ 
D)  $8 x^{6} y^{7}$ 
A)  $8 x^{7} y^{6}$ 
B)  $8 x y^{6}$ 
C)  $8 x y^{7}$ 
D)  $8 x^{6} y^{7}$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{x^{2}+15 x+51}{x+6}$

Accepted Answer

A)  $x+10$ 
B)  $x+9-\frac{3}{x+6}$ 
C)  $x+9+\frac{3}{x+6}$ 
D)  $\frac{x+9}{x+6}$ 
A)  $x+10$ 
B)  $x+9-\frac{3}{x+6}$ 
C)  $x+9+\frac{3}{x+6}$ 
D)  $\frac{x+9}{x+6}$

Question 12

The polynomial $0.0038 x^{3}-0.003 x^{2}+0.131 x+1.43$ gives the approximate total earnings of a company, in millions of dollars, where $x=0$ corresponds to $1996, x=1$ corresponds to 1997 , and so on. This model is valid for the years from 1996 to 2000. Determine the earnings for 1999. Round your answer to the nearest hundredth million.

Accepted Answer

A)  $\$ 2.15$ million 
B)  $\$ 1.71$ million 
C)  $\$ 1.95$ million 
D)  $\$ 1.9$ million 
A)  $\$ 2.15$ million 
B)  $\$ 1.71$ million 
C)  $\$ 1.95$ million 
D)  $\$ 1.9$ million

Question 13

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$.
-$f(x)=8 x+10$ and $g(x)=5 x-1$

Accepted Answer

A)  $40 x+2$ 
B)  $40 x+9$ 
C)  $40 x+18$ 
D)  $40 x+49$ 
A)  $40 x+2$ 
B)  $40 x+9$ 
C)  $40 x+18$ 
D)  $40 x+49$

Question 14

Tell whether the statement is .
-A monomial has no coefficient.

Accepted Answer

A)  Always 
B)  Never 
C)  Sometimes 
A)  Always 
B)  Never 
C)  Sometimes

Question 15

The polynomial $0.0056 x^{4}+0.006 x^{3}+0.0045 x^{2}+0.16 x+1.77$ gives the predicted sales volume of a company, in millions of items, where $x$ is the number of years from now. Determine the predicted sales 9 years from now. Round your answer to the nearest hundredth million.

Accepted Answer

A)  44.69 million 
B)  79.82 million 
C)  38.06 million 
D)  47.14 million 
A)  44.69 million 
B)  79.82 million 
C)  38.06 million 
D)  47.14 million

Question 16

If $p(x)=81 x^{5}-27 x^{4}+45 x^{2}$ and $q(x)=9 x^{2}$, find $\left(\frac{p}{q}\right)(-1)$.

Accepted Answer

A)  -7 
B)  17 
C)  -5 
D)  -17 
A)  -7 
B)  17 
C)  -5 
D)  -17

Question 17

Add or subtract as indicated.
-$\left(5 n^{5}+9 n-9 n^{3}\right)+\left(-3 n^{3}+8 n^{5}+4 n\right)$

Accepted Answer

A)  $14 \mathrm{n}^{9}$ 
B)  $13 n-12 n^{5}+13 n^{3}$ 
C)  $13 n^{5}-12 n^{3}+13 n$ 
D)  $17 n^{5}+2 n^{3}-5 n$ 
A)  $14 \mathrm{n}^{9}$ 
B)  $13 n-12 n^{5}+13 n^{3}$ 
C)  $13 n^{5}-12 n^{3}+13 n$ 
D)  $17 n^{5}+2 n^{3}-5 n$

Question 18

Find the product
-$12 a x^{5}\left(10 a x^{7}+5 x^{3}+11\right)$

Accepted Answer

A)  $-120 a^{2} x^{35}-60 a x^{15}-132 a x^{5}$ 
B)  $120 a^{2} x^{12}+60 a x^{8}+132 a x^{5}$ 
C)  $120 a x^{35}+60 a x^{15}+132 a x^{5}$ 
D)  $-120 a^{2} x^{12}-60 a x^{8}-132 a x^{5}$ 
A)  $-120 a^{2} x^{35}-60 a x^{15}-132 a x^{5}$ 
B)  $120 a^{2} x^{12}+60 a x^{8}+132 a x^{5}$ 
C)  $120 a x^{35}+60 a x^{15}+132 a x^{5}$ 
D)  $-120 a^{2} x^{12}-60 a x^{8}-132 a x^{5}$

Question 19

For the pair of functions, find the quotient $\left(\frac{f}{g}\right)(x)$ and give any $x$-values that are not in the domain of the quotient function.
-$f(x)=x^{2}+14 x+45, g(x)=x+5$

Accepted Answer

A)  $x+5 ; x \neq-9$ 
B)  $x+14 ; x \neq 0$ 
C)  $x+9 ; x \neq-5$ 
D)  $x+9 ; x \neq 5$ 
A)  $x+5 ; x \neq-9$ 
B)  $x+14 ; x \neq 0$ 
C)  $x+9 ; x \neq-5$ 
D)  $x+9 ; x \neq 5$

Question 20

If $\mathrm{p}(\mathrm{x})=18 \mathrm{x}^{3}-21 \mathrm{x}^{2}+72 \mathrm{x}-21$ and $\mathrm{q}(\mathrm{x})=9 \mathrm{x}+3$, find $\left(\frac{\mathrm{p}}{\mathrm{q}}\right)(3)$.

Accepted Answer

A)  2 
B)  $\frac{89}{5}$ 
C)  $\frac{82}{5}$ 
D)  0 
A)  2 
B)  $\frac{89}{5}$ 
C)  $\frac{82}{5}$ 
D)  0

For the given pair of functions, find the requested function. - $f(x)=5 x-3, g(x)=-7 x^{2}-16 x+9 ;(f-g)(x)$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $(-\mathrm{a})^{-18}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{-17}}{x^{-8}}$

Explain how you can use the special product $(a+b)(a-b)$ to find the product of $34 \cdot 26$ .

Provide an appropriate response. -Let $f(x)=x^{2}-7$ and $g(x)=2 x+6$ . Find $(f-g)(5)$ .

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(x^{3}\right)^{-3}$

Express the area of the figure as a polynomial in descending powers of the variable $x$ . -

Express the number in standard notation. - $3.448 \times 10^{-5}$

Decide whether the expression has been simplified correctly. - $(a b)^{2}=a^{2} b^{2}$

Find the product - $\left(-2 x^{4} y^{4}\right)\left(-4 x^{3} y^{2}\right)$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{x^{2}+15 x+51}{x+6}$

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=8 x+10$ and $g(x)=5 x-1$

Tell whether the statement is . -A monomial has no coefficient.

The polynomial $0.0056 x^{4}+0.006 x^{3}+0.0045 x^{2}+0.16 x+1.77$ gives the predicted sales volume of a company, in millions of items, where $x$ is the number of years from now. Determine the predicted sales 9 years from now. Round your answer to the nearest hundredth million.

If $p(x)=81 x^{5}-27 x^{4}+45 x^{2}$ and $q(x)=9 x^{2}$ , find $\left(\frac{p}{q}\right)(-1)$ .

Add or subtract as indicated. - $\left(5 n^{5}+9 n-9 n^{3}\right)+\left(-3 n^{3}+8 n^{5}+4 n\right)$

Find the product - $12 a x^{5}\left(10 a x^{7}+5 x^{3}+11\right)$

For the pair of functions, find the quotient $\left(\frac{f}{g}\right)(x)$ and give any $x$ -values that are not in the domain of the quotient function. - $f(x)=x^{2}+14 x+45, g(x)=x+5$

If $\mathrm{p}(\mathrm{x})=18 \mathrm{x}^{3}-21 \mathrm{x}^{2}+72 \mathrm{x}-21$ and $\mathrm{q}(\mathrm{x})=9 \mathrm{x}+3$ , find $\left(\frac{\mathrm{p}}{\mathrm{q}}\right)(3)$ .

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

For the given pair of functions, find the requested function. - f(x)=5x−3,g(x)=−7x2−16x+9;(f−g)(x)f(x)=5 x-3, g(x)=-7 x^{2}-16 x+9 ;(f-g)(x)f(x)=5x−3,g(x)=−7x2−16x+9;(f−g)(x)

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - (−a)−18(-\mathrm{a})^{-18}(−a)−18

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - x−17x−8\frac{x^{-17}}{x^{-8}}x−8x−17​

Explain how you can use the special product (a+b)(a−b)(a+b)(a-b)(a+b)(a−b) to find the product of 34⋅2634 \cdot 2634⋅26 .

Provide an appropriate response. -Let f(x)=x2−7f(x)=x^{2}-7f(x)=x2−7 and g(x)=2x+6g(x)=2 x+6g(x)=2x+6 . Find (f−g)(5)(f-g)(5)(f−g)(5) .

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers. - (x3)−3\left(x^{3}\right)^{-3}(x3)−3

Express the area of the figure as a polynomial in descending powers of the variable xxx . -

Express the number in standard notation. - 3.448×10−53.448 \times 10^{-5}3.448×10−5

Decide whether the expression has been simplified correctly. - (ab)2=a2b2(a b)^{2}=a^{2} b^{2}(ab)2=a2b2

Find the product - (−2x4y4)(−4x3y2)\left(-2 x^{4} y^{4}\right)\left(-4 x^{3} y^{2}\right)(−2x4y4)(−4x3y2)

Choose the one alternative that best completes the statement or answers the question. Divide - x2+15x+51x+6\frac{x^{2}+15 x+51}{x+6}x+6x2+15x+51​

Find ( f(g)(x)f(g)(x)f(g)(x) for the given functions f(x)f(x)f(x) and g(x)g(x)g(x) . - f(x)=8x+10f(x)=8 x+10f(x)=8x+10 and g(x)=5x−1g(x)=5 x-1g(x)=5x−1