Question 1

For the given pair of functions, find the requested function.
-$f(x)=x^{2}+4 x-2, g(x)=-7 x^{2}+7 x-8 ;(f-g)(x)$

Accepted Answer

A)  $8 x^{2}-10 x+14$ 
B)  $8 x^{2}-3 x+6$ 
C)  $-7 x^{2}-11 x+6$ 
D)  $-6 x^{2}+11 x-6$ 
A)  $8 x^{2}-10 x+14$ 
B)  $8 x^{2}-3 x+6$ 
C)  $-7 x^{2}-11 x+6$ 
D)  $-6 x^{2}+11 x-6$

Question 2

Give the numerical coefficient and the degree of the term.
-$5 z^{4}$

Accepted Answer

A)  Coefficient: 1 ; degree: 5 
B)  Coefficient: 5; degree: 1 
C)  Coefficient: 5; degree: 4 
D)  Coefficient: 4 ; degree: 5 
A)  Coefficient: 1 ; degree: 5 
B)  Coefficient: 5; degree: 1 
C)  Coefficient: 5; degree: 4 
D)  Coefficient: 4 ; degree: 5

Question 3

For the given pair of functions, find the requested function.
-$f(x)=x^{2}+4 x-3, g(x)=-9 x^{2}+7 x-8 ;(f+g)(x)$

Accepted Answer

A)  $-8 x^{2}-11 x-11$ 
B)  $-10 x^{2}+11 x+11$ 
C)  $-9 x^{2}+11 x+11$ 
D)  $-8 x^{2}+11 x-11$ 
A)  $-8 x^{2}-11 x-11$ 
B)  $-10 x^{2}+11 x+11$ 
C)  $-9 x^{2}+11 x+11$ 
D)  $-8 x^{2}+11 x-11$

Question 4

Evaluate the expression.
-$(-7)^{0}$

Accepted Answer

A)  -1 
B)  1 
C)  0 
D)  -7 
A)  -1 
B)  1 
C)  0 
D)  -7

Question 5

Perform the indicated operations.
-$\left(7 \mathrm{k}^{3}+2 \mathrm{k}^{2}-\mathrm{k}+7\right)-\left(4 \mathrm{k}^{3}-2 \mathrm{k}^{2}-\mathrm{k}-1\right)+\left(3 \mathrm{k}^{3}+6 \mathrm{k}^{2}-\mathrm{k}+1\right)$

Accepted Answer

A)  $6 k^{3}+10 k^{2}-k+9$ 
B)  $14 \mathrm{k}^{3}+10 \mathrm{k}^{2}-\mathrm{k}+9$ 
C)  $6 \mathrm{k}^{3}-10 \mathrm{k}^{2}+\mathrm{k}+8$ 
D)  $6 k^{3}+10 k^{2}+k+9$ 
A)  $6 k^{3}+10 k^{2}-k+9$ 
B)  $14 \mathrm{k}^{3}+10 \mathrm{k}^{2}-\mathrm{k}+9$ 
C)  $6 \mathrm{k}^{3}-10 \mathrm{k}^{2}+\mathrm{k}+8$ 
D)  $6 k^{3}+10 k^{2}+k+9$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{21 x^{5}+21 x^{4}+24 x^{3}}{3 x^{4}}$

Accepted Answer

A)  $15 x+7$ 
B)  $7 x+7$ 
C)  $7 x+21 x^{4}+\frac{8}{x}$ 
D)  $7 x+7+\frac{8}{x}$ 
A)  $15 x+7$ 
B)  $7 x+7$ 
C)  $7 x+21 x^{4}+\frac{8}{x}$ 
D)  $7 x+7+\frac{8}{x}$

Question 7

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.
-$f(x)=10 x^{2}+3 x-18, g(x)=5 x-6$

Accepted Answer

A)  $2 x+3 ; x \neq-\frac{6}{5}$ 
B)  $2 x+3 ; x \neq \frac{6}{5}$ 
C)  $2 x-3 ; x \neq-\frac{6}{5}$ 
D)  $2 x-3 ; x \neq \frac{6}{5}$ 
A)  $2 x+3 ; x \neq-\frac{6}{5}$ 
B)  $2 x+3 ; x \neq \frac{6}{5}$ 
C)  $2 x-3 ; x \neq-\frac{6}{5}$ 
D)  $2 x-3 ; x \neq \frac{6}{5}$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{42 x^{7}-24 x^{6}+42 x^{5}}{6 x^{6}}$

Accepted Answer

A)  $7 x-24 x^{6}+\frac{7}{x}$ 
B)  $14 x-4$ 
C)  $7 x-4$ 
D)  $7 x-4+\frac{7}{x}$ 
A)  $7 x-24 x^{6}+\frac{7}{x}$ 
B)  $14 x-4$ 
C)  $7 x-4$ 
D)  $7 x-4+\frac{7}{x}$

Question 9

Decide whether the expression has been simplified correctly.
-$x^{4} \cdot x^{5}=x^{9}$

Accepted Answer

A) True 
 B)False

Question 10

Express the number in standard notation.
-$-7.695 \times 10^{5}$

Accepted Answer

A)  $-7,695,000$ 
B)  $-76,950$ 
C)  $-76,950,000$ 
D)  $-769,500$ 
A)  $-7,695,000$ 
B)  $-76,950$ 
C)  $-76,950,000$ 
D)  $-769,500$

Question 11

Express the number in scientific notation
-$5,982,330$

Accepted Answer

A)  $5.98233 \times 10^{6}$ 
B)  $5.98233 \times 10^{-6}$ 
C)  $5.98233 \times 10^{1}$ 
D)  $5.98233 \times 10^{7}$ 
A)  $5.98233 \times 10^{6}$ 
B)  $5.98233 \times 10^{-6}$ 
C)  $5.98233 \times 10^{1}$ 
D)  $5.98233 \times 10^{7}$

Question 12

$P(s)=6 s^{3}+20 s^{2}-21 s-20$. What does the value of $P(5)$ tell you about the division problem below?

Accepted Answer

@#LAT-DLM&; thus, there will b

Question 13

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
-$m^{-9} m^{5} m^{-1}$

Accepted Answer

A)  $\frac{1}{m^{4}}$ 
B)  $\mathrm{m}^{7}$ 
C)  $\mathrm{m}^{5}$ 
D)  $\frac{1}{m^{5}}$ 
A)  $\frac{1}{m^{4}}$ 
B)  $\mathrm{m}^{7}$ 
C)  $\mathrm{m}^{5}$ 
D)  $\frac{1}{m^{5}}$

Question 14

Give the domain and range of the function.
-$f(x)=-4 x^{2}-2$

Accepted Answer

A)  Domain: $(-\infty, \infty)$; range: $(-2, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty,-2)$ 
C)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
D)  Domain: $(-4, \infty)$; range: $(2, \infty)$ 
A)  Domain: $(-\infty, \infty)$; range: $(-2, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty,-2)$ 
C)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
D)  Domain: $(-4, \infty)$; range: $(2, \infty)$

Question 15

$\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}$ gives the alcohol level in an average person's bloodstream $\mathrm{x}$ hours after drinking 8 oz of 100 -proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 7 hours?

Accepted Answer

A) True 
 B)False

Question 16

For the given pair of functions, find the requested function.
-$f(x)=3 x-4$ and $g(x)=-9 x^{2}-9 x+9 ;(f+g)(x)$

Accepted Answer

A)  $-10 x^{2}-6 x-5$ 
B)  $9 x^{2}-6 x-13$ 
C)  $-9 x^{2}+6 x+5$ 
D)  $-9 x^{2}-6 x+5$ 
A)  $-10 x^{2}-6 x-5$ 
B)  $9 x^{2}-6 x-13$ 
C)  $-9 x^{2}+6 x+5$ 
D)  $-9 x^{2}-6 x+5$

Question 17

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.
-$-7 x^{2}$

Accepted Answer

A)  Monomial; -7 
B)  Binomial; -7 
C)  Binomial; 0 
D)  Monomial; 2 
A)  Monomial; -7 
B)  Binomial; -7 
C)  Binomial; 0 
D)  Monomial; 2

Question 18

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$.
-$f(x)=7 x-6$ and $g(x)=6 x-8$

Accepted Answer

A)  $7 x+6$ 
B)  $12 x-14$ 
C)  $42 x-44$ 
D)  $42 x-62$ 
A)  $7 x+6$ 
B)  $12 x-14$ 
C)  $42 x-44$ 
D)  $42 x-62$

Question 19

Add or subtract as indicated.
-Subtract.
$ \begin{array}{r}-4 z^{2}-2 z-6 \ -9 z^{2}+5 z-10 \ \hline\end{array} $

Accepted Answer

A)  $-13 z^{2}+3 z-16$ 
B)  $5 z^{2}-7 z+4$ 
C)  $13 z^{2}-3 z+16$ 
D)  $-5 z^{2}+7 z-4$ 
A)  $-13 z^{2}+3 z-16$ 
B)  $5 z^{2}-7 z+4$ 
C)  $13 z^{2}-3 z+16$ 
D)  $-5 z^{2}+7 z-4$

Question 20

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

Accepted Answer

A)  $8 s^{4}-10 s^{3}-18 s^{2}-6 s+12$ 
B)  $8 s^{4}-10 s^{3}-18 s^{2}+6 s+12$ 
C)  $8 s^{4}-6 s^{3}-18 s^{2}+6 s+12$ 
D)  $8 s^{4}-10 s^{3}+6 s^{2}+6 s+12$ 
A)  $8 s^{4}-10 s^{3}-18 s^{2}-6 s+12$ 
B)  $8 s^{4}-10 s^{3}-18 s^{2}+6 s+12$ 
C)  $8 s^{4}-6 s^{3}-18 s^{2}+6 s+12$ 
D)  $8 s^{4}-10 s^{3}+6 s^{2}+6 s+12$

For the given pair of functions, find the requested function. - $f(x)=x^{2}+4 x-2, g(x)=-7 x^{2}+7 x-8 ;(f-g)(x)$

Give the numerical coefficient and the degree of the term. - $5 z^{4}$

For the given pair of functions, find the requested function. - $f(x)=x^{2}+4 x-3, g(x)=-9 x^{2}+7 x-8 ;(f+g)(x)$

Evaluate the expression. - $(-7)^{0}$

Perform the indicated operations. - $\left(7 \mathrm{k}^{3}+2 \mathrm{k}^{2}-\mathrm{k}+7\right)-\left(4 \mathrm{k}^{3}-2 \mathrm{k}^{2}-\mathrm{k}-1\right)+\left(3 \mathrm{k}^{3}+6 \mathrm{k}^{2}-\mathrm{k}+1\right)$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{21 x^{5}+21 x^{4}+24 x^{3}}{3 x^{4}}$

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. - $f(x)=10 x^{2}+3 x-18, g(x)=5 x-6$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{42 x^{7}-24 x^{6}+42 x^{5}}{6 x^{6}}$

Decide whether the expression has been simplified correctly. - $x^{4} \cdot x^{5}=x^{9}$

Express the number in standard notation. - $-7.695 \times 10^{5}$

Express the number in scientific notation - $5,982,330$

$P(s)=6 s^{3}+20 s^{2}-21 s-20$ . What does the value of $P(5)$ tell you about the division problem below? $P(s)=6 s^{3}+20 s^{2}-21 s-20 . What does the value of P(5) tell you about the division problem below?$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $m^{-9} m^{5} m^{-1}$

Give the domain and range of the function. - $f(x)=-4 x^{2}-2$

$\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}$ gives the alcohol level in an average person's bloodstream $\mathrm{x}$ hours after drinking 8 oz of 100 -proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 7 hours?

For the given pair of functions, find the requested function. - $f(x)=3 x-4$ and $g(x)=-9 x^{2}-9 x+9 ;(f+g)(x)$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-7 x^{2}$

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=7 x-6$ and $g(x)=6 x-8$

Add or subtract as indicated. -Subtract. -4-2z-6 -9+5z-10

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

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)=x2+4x−2,g(x)=−7x2+7x−8;(f−g)(x)f(x)=x^{2}+4 x-2, g(x)=-7 x^{2}+7 x-8 ;(f-g)(x)f(x)=x2+4x−2,g(x)=−7x2+7x−8;(f−g)(x)

Give the numerical coefficient and the degree of the term. - 5z45 z^{4}5z4

For the given pair of functions, find the requested function. - f(x)=x2+4x−3,g(x)=−9x2+7x−8;(f+g)(x)f(x)=x^{2}+4 x-3, g(x)=-9 x^{2}+7 x-8 ;(f+g)(x)f(x)=x2+4x−3,g(x)=−9x2+7x−8;(f+g)(x)

Evaluate the expression. - (−7)0(-7)^{0}(−7)0

Choose the one alternative that best completes the statement or answers the question. Divide - 21x5+21x4+24x33x4\frac{21 x^{5}+21 x^{4}+24 x^{3}}{3 x^{4}}3x421x5+21x4+24x3​

For the pair of functions, find the quotient (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) and give any xxx -values that are not in the domain of the quotient function. - f(x)=10x2+3x−18,g(x)=5x−6f(x)=10 x^{2}+3 x-18, g(x)=5 x-6f(x)=10x2+3x−18,g(x)=5x−6

Choose the one alternative that best completes the statement or answers the question. Divide - 42x7−24x6+42x56x6\frac{42 x^{7}-24 x^{6}+42 x^{5}}{6 x^{6}}6x642x7−24x6+42x5​

Decide whether the expression has been simplified correctly. - x4⋅x5=x9x^{4} \cdot x^{5}=x^{9}x4⋅x5=x9

Express the number in standard notation. - −7.695×105-7.695 \times 10^{5}−7.695×105

Express the number in scientific notation - 5,982,3305,982,3305,982,330

P(s)=6s3+20s2−21s−20P(s)=6 s^{3}+20 s^{2}-21 s-20P(s)=6s3+20s2−21s−20 . What does the value of P(5)P(5)P(5) tell you about the division problem below?

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - m−9m5m−1m^{-9} m^{5} m^{-1}m−9m5m−1

Give the domain and range of the function. - f(x)=−4x2−2f(x)=-4 x^{2}-2f(x)=−4x2−2

For the given pair of functions, find the requested function. - f(x)=3x−4f(x)=3 x-4f(x)=3x−4 and g(x)=−9x2−9x+9;(f+g)(x)g(x)=-9 x^{2}-9 x+9 ;(f+g)(x)g(x)=−9x2−9x+9;(f+g)(x)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - −7x2-7 x^{2}−7x2

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)=7x−6f(x)=7 x-6f(x)=7x−6 and g(x)=6x−8g(x)=6 x-8g(x)=6x−8