Question 1

Find the product
-$(2 x+3)(x-8)$

Accepted Answer

A)  $x^{2}-24 x-13$ 
B)  $x^{2}-13 x-14$ 
C)  $2 x^{2}-13 x-24$ 
D)  $2 x^{2}-14 x-24$ 
A)  $x^{2}-24 x-13$ 
B)  $x^{2}-13 x-14$ 
C)  $2 x^{2}-13 x-24$ 
D)  $2 x^{2}-14 x-24$

Question 2

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$.
-$f(x)=3 x+5$ and $g(x)=-5 x+3$

Accepted Answer

A)  $-15 x$ 
B)  $15 x+14$ 
C)  $-15 x+14$ 
D)  $-15 x+28$ 
A)  $-15 x$ 
B)  $15 x+14$ 
C)  $-15 x+14$ 
D)  $-15 x+28$

Question 3

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(2 x^{3} y^{5}\right)^{2}\left(5 y^{3}\right)^{3}$

Accepted Answer

A)  $10 x^{6} y^{19}$ 
B)  $10 x^{3} y^{8}$ 
C)  $500 x^{6} y^{19}$ 
D)  $500 x^{5} y^{13}$ 
A)  $10 x^{6} y^{19}$ 
B)  $10 x^{3} y^{8}$ 
C)  $500 x^{6} y^{19}$ 
D)  $500 x^{5} y^{13}$

Question 4

Combine terms.
-$n^{3}-10 n^{4}+10 n^{2}+n^{4}-5 n^{3}$

Accepted Answer

A)  $-9 n^{4}-4 n^{3}+10 n^{2}$ 
B)  $9 n^{4}+4 n^{3}-10 n^{2}$ 
C)  $-10 n^{4}+n^{3}+10 n^{2}$ 
D)  $-9 n^{8}-4 n^{6}+10 n^{2}$ 
A)  $-9 n^{4}-4 n^{3}+10 n^{2}$ 
B)  $9 n^{4}+4 n^{3}-10 n^{2}$ 
C)  $-10 n^{4}+n^{3}+10 n^{2}$ 
D)  $-9 n^{8}-4 n^{6}+10 n^{2}$

Question 5

If the following division problem has no remainder, what does that tell you about the given fraction?

$\frac{8 r^{4}+30 r^{3}+33 r^{2}+8 r-30}{8 r^{2}+28 r+20}$

Accepted Answer

The fraction can be

Question 6

Perform the indicated operations.
-$(2 x-5 y)^{2}$

Accepted Answer

A)  $4 x^{2}+25 y^{2}$ 
B)  $2 x^{2}+25 y^{2}$ 
C)  $2 x^{2}-20 x y+25 y^{2}$ 
D)  $4 x^{2}-20 x y+25 y^{2}$ 
A)  $4 x^{2}+25 y^{2}$ 
B)  $2 x^{2}+25 y^{2}$ 
C)  $2 x^{2}-20 x y+25 y^{2}$ 
D)  $4 x^{2}-20 x y+25 y^{2}$

Question 7

Are the two expressions equivalent? Give numerical values for $x$ and $y$ to back up your answer.
$(x+y)^{4} ; x^{4}+y^{4}$

Accepted Answer

The two expressions are not eq

Question 8

Find the product
-$-8 a x^{7}\left(9 a x^{6}-12 x^{2}-8 a\right)$

Accepted Answer

A)  $-72 a^{2} x^{42}+96 a x^{14}+64 a^{2} x^{7}$ 
B)  $-72 a^{2} x^{13}+96 a x^{9}+64 a^{2} x^{7}$ 
C)  $-72 a x^{13}+96 a x^{9}+64 a x^{7}$ 
D)  $-72 a^{2} x^{13}-96 a x^{9}-64 a^{2} x^{7}$ 
A)  $-72 a^{2} x^{42}+96 a x^{14}+64 a^{2} x^{7}$ 
B)  $-72 a^{2} x^{13}+96 a x^{9}+64 a^{2} x^{7}$ 
C)  $-72 a x^{13}+96 a x^{9}+64 a x^{7}$ 
D)  $-72 a^{2} x^{13}-96 a x^{9}-64 a^{2} x^{7}$

Question 9

Write the polynomial in descending powers of the variable.
-$-32-x^{9}-11 x^{3}+41 x$

Accepted Answer

A)  $41 x-32-11 x^{3}-x^{9}$ 
B)  $-x^{9}-11 x^{3}+41 x-32$ 
C)  $x^{9}+11 x^{3}-41 x-32$ 
D)  $-32+41 x-11 x^{3}-x^{9}$ 
A)  $41 x-32-11 x^{3}-x^{9}$ 
B)  $-x^{9}-11 x^{3}+41 x-32$ 
C)  $x^{9}+11 x^{3}-41 x-32$ 
D)  $-32+41 x-11 x^{3}-x^{9}$

Question 10

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.
-$\frac{x^{-8}}{x^{-19}}$

Accepted Answer

A)  $x^{11}$ 
B)  $\frac{1}{x^{11}}$ 
C)  $\frac{1}{x^{27}}$ 
D)  $-x^{11}$ 
A)  $x^{11}$ 
B)  $\frac{1}{x^{11}}$ 
C)  $\frac{1}{x^{27}}$ 
D)  $-x^{11}$

Question 11

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.
-$-17 s^{7}+6 s-5$

Accepted Answer

A)  Trinomial; 8 
B)  Binomial; 8 
C)  Trinomial; 7 
D)  None of these; 9 
A)  Trinomial; 8 
B)  Binomial; 8 
C)  Trinomial; 7 
D)  None of these; 9

Question 12

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.
-$(3 p)^{-3}$

Accepted Answer

A)  $\frac{1}{9 p^{-3}}$ 
B)  $\frac{1}{27 p^{3}}$ 
C)  $\frac{1}{-9 p^{3}}$ 
D)  $\frac{1}{3 p^{3}}$ 
A)  $\frac{1}{9 p^{-3}}$ 
B)  $\frac{1}{27 p^{3}}$ 
C)  $\frac{1}{-9 p^{3}}$ 
D)  $\frac{1}{3 p^{3}}$

Question 13

$(0.6 x-1.2 y)^{2}$

Accepted Answer

A)  $0.36 x^{2}-1.44 y^{2}$ 
B)  $0.36 x^{2}+1.44 y^{2}$ 
C)  $0.36 x^{2}+1.44 x y+1.44 y^{2}$ 
D)  $0.36 x^{2}-1.44 x y+1.44 y^{2}$ 
A)  $0.36 x^{2}-1.44 y^{2}$ 
B)  $0.36 x^{2}+1.44 y^{2}$ 
C)  $0.36 x^{2}+1.44 x y+1.44 y^{2}$ 
D)  $0.36 x^{2}-1.44 x y+1.44 y^{2}$

Question 14

Add or subtract as indicated.
-Add.
$ \begin{array}{c}6 m^{3}-8 m+5 \ -2 m^{3}+12 m+8\end{array} $

Accepted Answer

A)  $4 m^{3}+4 m+13$ 
B)  $-34 m+20 m+3$ 
C)  $8 \mathrm{~m}-20 \mathrm{~m}-3$ 
D)  $-33 m^{3}-4 m-13$ 
A)  $4 m^{3}+4 m+13$ 
B)  $-34 m+20 m+3$ 
C)  $8 \mathrm{~m}-20 \mathrm{~m}-3$ 
D)  $-33 m^{3}-4 m-13$

Question 15

Express the number in standard notation.
-$2.89 \times 10^{-4}$

Accepted Answer

A)  0.0000289 
B)  $-289,000$ 
C)  0.000289 
D)  0.00289 
A)  0.0000289 
B)  $-289,000$ 
C)  0.000289 
D)  0.00289

Question 16

Express the number in standard notation.
-$1.090 \times 10^{5}$

Accepted Answer

A)  54.5 
B)  109,000 
C)  10,900 
D)  $1,090,000$ 
A)  54.5 
B)  109,000 
C)  10,900 
D)  $1,090,000$

Question 17

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.
-$f(x)=27 x^{3}-216, g(x)=3 x-6$

Accepted Answer

A)  $3 x^{2}+6 x+36 ; x \neq-2$ 
B)  $9 x^{2}-18 x+36 ; x \neq 0$ 
C)  $10 x^{2}+20 x+35 ; x \neq 2$ 
D)  $9 x^{2}+18 x+36 ; x \neq 2$ 
A)  $3 x^{2}+6 x+36 ; x \neq-2$ 
B)  $9 x^{2}-18 x+36 ; x \neq 0$ 
C)  $10 x^{2}+20 x+35 ; x \neq 2$ 
D)  $9 x^{2}+18 x+36 ; x \neq 2$

Question 18

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.
-$f(x)=64 x^{3}+8, g(x)=4 x+2$

Accepted Answer

A)  $4 x^{2}+8 x+4 ; x \neq \frac{1}{2}$ 
B)  $18 x^{2}-7 x+4 ; x \neq-2$ 
C)  $16 x^{2}+8 x+4 ; x \neq-\frac{1}{2}$ 
D)  $16 x^{2}-8 x+4 ; x \neq-\frac{1}{2}$ 
A)  $4 x^{2}+8 x+4 ; x \neq \frac{1}{2}$ 
B)  $18 x^{2}-7 x+4 ; x \neq-2$ 
C)  $16 x^{2}+8 x+4 ; x \neq-\frac{1}{2}$ 
D)  $16 x^{2}-8 x+4 ; x \neq-\frac{1}{2}$

Question 19

Graph the function.
-$ f(x)=x^{2}+3 x-8 $

Accepted Answer

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

Question 20

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.
-$-7 z^{5}-4 z^{4}-6 z^{3}+12$

Accepted Answer

A)  Trinomial; 12 
B)  None of these; 5 
C)  Binomial; 13 
D)  Trinomial; 5 
A)  Trinomial; 12 
B)  None of these; 5 
C)  Binomial; 13 
D)  Trinomial; 5

Find the product - $(2 x+3)(x-8)$

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=3 x+5$ and $g(x)=-5 x+3$

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(2 x^{3} y^{5}\right)^{2}\left(5 y^{3}\right)^{3}$

Combine terms. - $n^{3}-10 n^{4}+10 n^{2}+n^{4}-5 n^{3}$

Perform the indicated operations. - $(2 x-5 y)^{2}$

Are the two expressions equivalent? Give numerical values for $x$ and $y$ to back up your answer. $(x+y)^{4} ; x^{4}+y^{4}$

Find the product - $-8 a x^{7}\left(9 a x^{6}-12 x^{2}-8 a\right)$

Write the polynomial in descending powers of the variable. - $-32-x^{9}-11 x^{3}+41 x$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{-8}}{x^{-19}}$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-17 s^{7}+6 s-5$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $(3 p)^{-3}$

$(0.6 x-1.2 y)^{2}$

Add or subtract as indicated. -Add. 6-8m+5 -2+12m+8

Express the number in standard notation. - $2.89 \times 10^{-4}$

Express the number in standard notation. - $1.090 \times 10^{5}$

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. - $f(x)=27 x^{3}-216, g(x)=3 x-6$

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. - $f(x)=64 x^{3}+8, g(x)=4 x+2$

Graph the function. - $f(x)=x^{2}+3 x-8$ $Graph the function. - f(x)=x^{2}+3 x-8$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-7 z^{5}-4 z^{4}-6 z^{3}+12$

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

Find the product - (2x+3)(x−8)(2 x+3)(x-8)(2x+3)(x−8)

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)=3x+5f(x)=3 x+5f(x)=3x+5 and g(x)=−5x+3g(x)=-5 x+3g(x)=−5x+3

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - (2x3y5)2(5y3)3\left(2 x^{3} y^{5}\right)^{2}\left(5 y^{3}\right)^{3}(2x3y5)2(5y3)3

Combine terms. - n3−10n4+10n2+n4−5n3n^{3}-10 n^{4}+10 n^{2}+n^{4}-5 n^{3}n3−10n4+10n2+n4−5n3

If the following division problem has no remainder, what does that tell you about the given fraction? 8r4+30r3+33r2+8r−308r2+28r+20\frac{8 r^{4}+30 r^{3}+33 r^{2}+8 r-30}{8 r^{2}+28 r+20}8r2+28r+208r4+30r3+33r2+8r−30​

Perform the indicated operations. - (2x−5y)2(2 x-5 y)^{2}(2x−5y)2

Are the two expressions equivalent? Give numerical values for xxx and yyy to back up your answer. (x+y)4;x4+y4(x+y)^{4} ; x^{4}+y^{4}(x+y)4;x4+y4

Find the product - −8ax7(9ax6−12x2−8a)-8 a x^{7}\left(9 a x^{6}-12 x^{2}-8 a\right)−8ax7(9ax6−12x2−8a)

Write the polynomial in descending powers of the variable. - −32−x9−11x3+41x-32-x^{9}-11 x^{3}+41 x−32−x9−11x3+41x

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - x−8x−19\frac{x^{-8}}{x^{-19}}x−19x−8​

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - −17s7+6s−5-17 s^{7}+6 s-5−17s7+6s−5

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - (3p)−3(3 p)^{-3}(3p)−3

(0.6x−1.2y)2(0.6 x-1.2 y)^{2}(0.6x−1.2y)2

Add or subtract as indicated. -Add. 6-8m+5 -2+12m+8

Express the number in standard notation. - 2.89×10−42.89 \times 10^{-4}2.89×10−4

Express the number in standard notation. - 1.090×1051.090 \times 10^{5}1.090×105

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)=27x3−216,g(x)=3x−6f(x)=27 x^{3}-216, g(x)=3 x-6f(x)=27x3−216,g(x)=3x−6

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)=64x3+8,g(x)=4x+2f(x)=64 x^{3}+8, g(x)=4 x+2f(x)=64x3+8,g(x)=4x+2

Graph the function. - f(x)=x2+3x−8 f(x)=x^{2}+3 x-8 f(x)=x2+3x−8

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - −7z5−4z4−6z3+12-7 z^{5}-4 z^{4}-6 z^{3}+12−7z5−4z4−6z3+12

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

Find the product - $(2 x+3)(x-8)$

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=3 x+5$ and $g(x)=-5 x+3$

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(2 x^{3} y^{5}\right)^{2}\left(5 y^{3}\right)^{3}$

Combine terms. - $n^{3}-10 n^{4}+10 n^{2}+n^{4}-5 n^{3}$

Perform the indicated operations. - $(2 x-5 y)^{2}$

Are the two expressions equivalent? Give numerical values for $x$ and $y$ to back up your answer. $(x+y)^{4} ; x^{4}+y^{4}$

Find the product - $-8 a x^{7}\left(9 a x^{6}-12 x^{2}-8 a\right)$

Write the polynomial in descending powers of the variable. - $-32-x^{9}-11 x^{3}+41 x$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{-8}}{x^{-19}}$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-17 s^{7}+6 s-5$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $(3 p)^{-3}$

$(0.6 x-1.2 y)^{2}$

Express the number in standard notation. - $2.89 \times 10^{-4}$

Express the number in standard notation. - $1.090 \times 10^{5}$

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. - $f(x)=27 x^{3}-216, g(x)=3 x-6$

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. - $f(x)=64 x^{3}+8, g(x)=4 x+2$

Graph the function. - $f(x)=x^{2}+3 x-8$ $Graph the function. - f(x)=x^{2}+3 x-8$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-7 z^{5}-4 z^{4}-6 z^{3}+12$