Question 1

For the given pair of functions, find the requested function.
-If $f(x)=x^{2}+9 x+7$ and $g(x)=6 x-2$, find (fg)(4).

Accepted Answer

A)  -366 
B)  1250 
C)  1298 
D)  209 
A)  -366 
B)  1250 
C)  1298 
D)  209

Question 2

Evaluate the composition of functions.
-Let $f(x)=8 x+2$ and $g(x)=x+6$. Find $(f \circ g)(3)$.

Accepted Answer

A)  234 
B)  74 
C)  32 
D)  35 
A)  234 
B)  74 
C)  32 
D)  35

Question 3

Evaluate the expression.
-$\frac{1}{8^{-3}}$

Accepted Answer

A)  512 
B)  4096 
C)  64 
D)  24 
A)  512 
B)  4096 
C)  64 
D)  24

Question 4

Does scientific notation allow a negative number to be multiplied by a power of 10 ?

Accepted Answer

A) True 
 B)False

Question 5

Combine terms.
-$8 q^{4}-3 q^{4}$

Accepted Answer

A)  $-24 q^{4}$ 
B)  $-24 q^{8}$ 
C)  $5 q^{4}$ 
D)  $5 q^{8}$ 
A)  $-24 q^{4}$ 
B)  $-24 q^{8}$ 
C)  $5 q^{4}$ 
D)  $5 q^{8}$

Question 6

Express the number in standard notation.
-$7.3714 \times 10^{6}$

Accepted Answer

A)  442.284 
B)  $73,714,000$ 
C)  737,140 
D)  $7,371,400$ 
A)  442.284 
B)  $73,714,000$ 
C)  737,140 
D)  $7,371,400$

Question 7

Add or subtract as indicated.
-$\left(-3+2 x^{6}+7 x^{8}+8 x^{7}\right)+\left(-4 x^{7}+4 x^{6}+2+2 x^{8}\right)$

Accepted Answer

A)  $-7 x^{8}-7 x^{7}+9 x^{6}+10$ 
B)  $9 x^{16}+4 x^{14}+6 x^{12}-1$ 
C)  $9 x^{8}+4 x^{7}+6 x^{6}-1$ 
D)  $19 x^{42}-1$ 
A)  $-7 x^{8}-7 x^{7}+9 x^{6}+10$ 
B)  $9 x^{16}+4 x^{14}+6 x^{12}-1$ 
C)  $9 x^{8}+4 x^{7}+6 x^{6}-1$ 
D)  $19 x^{42}-1$

Question 8

Give an example of two polynomials which can be multiplied by the FOIL method. Use your example to explain the method.

Accepted Answer

Answers will vary, b

Question 9

Choose the one alternative that best completes the statement or answers the question
-$\frac{5^{-1}}{3^{-1}}$

Accepted Answer

A)  1 
B)  $\frac{3}{5}$ 
C)  $-\frac{3}{5}$ 
D)  $\frac{5}{3}$ 
A)  1 
B)  $\frac{3}{5}$ 
C)  $-\frac{3}{5}$ 
D)  $\frac{5}{3}$

Question 10

Find the product
-$(p+5 q)(p-5 q)$

Accepted Answer

A)  $p^{2}-10 q^{2}$ 
B)  $p^{2}-10 p q-25 q^{2}$ 
C)  $p^{2}-25 q^{2}$ 
D)  $p^{2}+10 p q-25 q^{2}$ 
A)  $p^{2}-10 q^{2}$ 
B)  $p^{2}-10 p q-25 q^{2}$ 
C)  $p^{2}-25 q^{2}$ 
D)  $p^{2}+10 p q-25 q^{2}$

Question 11

Tell whether the statement is .
-A binomial is a polynomial.

Accepted Answer

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

Question 12

Find the product
-$(13 r-5)(13 r+5)$

Accepted Answer

A)  $169+130 \mathrm{r}-25 \mathrm{r}^{2}$ 
B)  $169 r^{2}-130 r-25$ 
C)  $169 r^{2}-25$ 
D)  $13 \mathrm{r}^{2}-25$ 
A)  $169+130 \mathrm{r}-25 \mathrm{r}^{2}$ 
B)  $169 r^{2}-130 r-25$ 
C)  $169 r^{2}-25$ 
D)  $13 \mathrm{r}^{2}-25$

Question 13

Use scientific notation to simplify. Write the answer in both scientific notation and standard notation.
-$\frac{49,000 \times 0.0004}{0.007 \times 7,000,000}$

Accepted Answer

A)  $4 \times 10^{-4} ; 0.0004$ 
B)  $4 \times 10^{-3} ; 0.004$ 
C)  $4 \times 10^{-2} ; 0.04$ 
D)  $0.4 \times 10^{-3} ; 0.004$ 
A)  $4 \times 10^{-4} ; 0.0004$ 
B)  $4 \times 10^{-3} ; 0.004$ 
C)  $4 \times 10^{-2} ; 0.04$ 
D)  $0.4 \times 10^{-3} ; 0.004$

Question 14

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.
-$\frac{x^{19}}{x^{5}}$

Accepted Answer

A)  $x^{24}$ 
B)  $x^{14}$ 
C)  $\frac{1}{x^{14}}$ 
D)  $-x^{14}$ 
A)  $x^{24}$ 
B)  $x^{14}$ 
C)  $\frac{1}{x^{14}}$ 
D)  $-x^{14}$

Question 15

A balloon in the shape of a sphere is deflating. Given that $t$ represents the time, in minutes, since it began losing air, the radius of the balloon (in $\mathrm{cm}$ ) is $r(t)=20-\mathrm{t}$. Let the equation $\mathrm{V}(\mathrm{r})=\frac{4}{3} \pi \mathrm{r}^{3}$ represent the volume of a sphere of radius $r$. Find and interpret $(\mathrm{V} \circ \mathrm{r})(\mathrm{t})$.

Accepted Answer

A)  $(V \circ r)(t)=20-\frac{4}{3} \pi(20-t)^{3}$; this is the volume of the air lost by the balloon (in $\mathrm{cm}^{3}$ ) as a function of time (in minutes). 
B)  $(V \circ r)(t)=\frac{4}{3} \pi(20-t)^{3}$; this is the volume of the air lost by the balloon (in $\left.\mathrm{cm}^{3}\right)$ as a function of time (in minutes). 
C)  $(V \circ r)(t)=\frac{4}{3} \pi(20-t)^{3}$; this is the volume of the balloon (in $\left.\mathrm{cm}^{3}\right)$ as a function of time (in minutes). 
D)  $(\mathrm{V} \circ \mathrm{r})(\mathrm{t})=\frac{4}{3} \pi(\mathrm{t}-20)^{3}$; this is the volume of the balloon (in $\mathrm{cm}^{3}$ ) as a function of time (in minutes). 
A)  $(V \circ r)(t)=20-\frac{4}{3} \pi(20-t)^{3}$; this is the volume of the air lost by the balloon (in $\mathrm{cm}^{3}$ ) as a function of time (in minutes). 
B)  $(V \circ r)(t)=\frac{4}{3} \pi(20-t)^{3}$; this is the volume of the air lost by the balloon (in $\left.\mathrm{cm}^{3}\right)$ as a function of time (in minutes). 
C)  $(V \circ r)(t)=\frac{4}{3} \pi(20-t)^{3}$; this is the volume of the balloon (in $\left.\mathrm{cm}^{3}\right)$ as a function of time (in minutes). 
D)  $(\mathrm{V} \circ \mathrm{r})(\mathrm{t})=\frac{4}{3} \pi(\mathrm{t}-20)^{3}$; this is the volume of the balloon (in $\mathrm{cm}^{3}$ ) as a function of time (in minutes).

Question 16

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.
-$8^{-7}$

Accepted Answer

A)  $-8^{1 / 7}$ 
B)  $-\frac{1}{8^{7}}$ 
C)  $\frac{1}{8^{7}}$ 
D)  $-8^{7}$ 
A)  $-8^{1 / 7}$ 
B)  $-\frac{1}{8^{7}}$ 
C)  $\frac{1}{8^{7}}$ 
D)  $-8^{7}$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\left(2 y^{2}-\frac{25}{3} y-3\right) \div(9 y+3)$

Accepted Answer

A)  $y^{2}-75 y-1$ 
B)  $\frac{2}{9} y+1$ 
C)  $\frac{2}{9} y-1$ 
D)  $-7 y^{2}-\frac{34}{3} y-3$ 
A)  $y^{2}-75 y-1$ 
B)  $\frac{2}{9} y+1$ 
C)  $\frac{2}{9} y-1$ 
D)  $-7 y^{2}-\frac{34}{3} y-3$

Question 18

Evaluate the composition of functions.
-Let $f(x)=x^{2}+2$ and $g(x)=3 x+6$. Find $(g \circ f)(5)$.

Accepted Answer

A)  33 
B)  87 
C)  75 
D)  443 
A)  33 
B)  87 
C)  75 
D)  443

Question 19

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.
-$-8 a^{3}$

Accepted Answer

A)  Monomial; 3 
B)  None of these; -8 
C)  Monomial; -8 
D)  Binomial; 3 
A)  Monomial; 3 
B)  None of these; -8 
C)  Monomial; -8 
D)  Binomial; 3

Question 20

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.
-$\mathrm{r}^{-3}$

Accepted Answer

A)  $\mathrm{r}^{1 / 3}$ 
B)  $\frac{1}{r^{3}}$ 
C)  $-\frac{1}{r^{3}}$ 
D)  $-r^{3}$ 
A)  $\mathrm{r}^{1 / 3}$ 
B)  $\frac{1}{r^{3}}$ 
C)  $-\frac{1}{r^{3}}$ 
D)  $-r^{3}$

For the given pair of functions, find the requested function. -If $f(x)=x^{2}+9 x+7$ and $g(x)=6 x-2$ , find (fg)(4).

Evaluate the composition of functions. -Let $f(x)=8 x+2$ and $g(x)=x+6$ . Find $(f \circ g)(3)$ .

Evaluate the expression. - $\frac{1}{8^{-3}}$

Does scientific notation allow a negative number to be multiplied by a power of 10 ?

Combine terms. - $8 q^{4}-3 q^{4}$

Express the number in standard notation. - $7.3714 \times 10^{6}$

Add or subtract as indicated. - $\left(-3+2 x^{6}+7 x^{8}+8 x^{7}\right)+\left(-4 x^{7}+4 x^{6}+2+2 x^{8}\right)$

Give an example of two polynomials which can be multiplied by the FOIL method. Use your example to explain the method.

Choose the one alternative that best completes the statement or answers the question - $\frac{5^{-1}}{3^{-1}}$

Find the product - $(p+5 q)(p-5 q)$

Tell whether the statement is . -A binomial is a polynomial.

Find the product - $(13 r-5)(13 r+5)$

Use scientific notation to simplify. Write the answer in both scientific notation and standard notation. - $\frac{49,000 \times 0.0004}{0.007 \times 7,000,000}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{19}}{x^{5}}$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $8^{-7}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 y^{2}-\frac{25}{3} y-3\right) \div(9 y+3)$

Evaluate the composition of functions. -Let $f(x)=x^{2}+2$ and $g(x)=3 x+6$ . Find $(g \circ f)(5)$ .

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-8 a^{3}$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $\mathrm{r}^{-3}$

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. -If f(x)=x2+9x+7f(x)=x^{2}+9 x+7f(x)=x2+9x+7 and g(x)=6x−2g(x)=6 x-2g(x)=6x−2 , find (fg)(4).

Evaluate the composition of functions. -Let f(x)=8x+2f(x)=8 x+2f(x)=8x+2 and g(x)=x+6g(x)=x+6g(x)=x+6 . Find (f∘g)(3)(f \circ g)(3)(f∘g)(3) .

Evaluate the expression. - 18−3\frac{1}{8^{-3}}8−31​

Does scientific notation allow a negative number to be multiplied by a power of 10 ?

Combine terms. - 8q4−3q48 q^{4}-3 q^{4}8q4−3q4

Express the number in standard notation. - 7.3714×1067.3714 \times 10^{6}7.3714×106

Add or subtract as indicated. - (−3+2x6+7x8+8x7)+(−4x7+4x6+2+2x8)\left(-3+2 x^{6}+7 x^{8}+8 x^{7}\right)+\left(-4 x^{7}+4 x^{6}+2+2 x^{8}\right)(−3+2x6+7x8+8x7)+(−4x7+4x6+2+2x8)

Give an example of two polynomials which can be multiplied by the FOIL method. Use your example to explain the method.

Choose the one alternative that best completes the statement or answers the question - 5−13−1\frac{5^{-1}}{3^{-1}}3−15−1​

Find the product - (p+5q)(p−5q)(p+5 q)(p-5 q)(p+5q)(p−5q)

Tell whether the statement is . -A binomial is a polynomial.

Find the product - (13r−5)(13r+5)(13 r-5)(13 r+5)(13r−5)(13r+5)

Use scientific notation to simplify. Write the answer in both scientific notation and standard notation. - 49,000×0.00040.007×7,000,000\frac{49,000 \times 0.0004}{0.007 \times 7,000,000}0.007×7,000,00049,000×0.0004​

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - x19x5\frac{x^{19}}{x^{5}}x5x19​

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - 8−78^{-7}8−7

Choose the one alternative that best completes the statement or answers the question. Divide - (2y2−253y−3)÷(9y+3)\left(2 y^{2}-\frac{25}{3} y-3\right) \div(9 y+3)(2y2−325​y−3)÷(9y+3)

Evaluate the composition of functions. -Let f(x)=x2+2f(x)=x^{2}+2f(x)=x2+2 and g(x)=3x+6g(x)=3 x+6g(x)=3x+6 . Find (g∘f)(5)(g \circ f)(5)(g∘f)(5) .

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - −8a3-8 a^{3}−8a3

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - r−3\mathrm{r}^{-3}r−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

For the given pair of functions, find the requested function. -If $f(x)=x^{2}+9 x+7$ and $g(x)=6 x-2$ , find (fg)(4).

Evaluate the composition of functions. -Let $f(x)=8 x+2$ and $g(x)=x+6$ . Find $(f \circ g)(3)$ .

Evaluate the expression. - $\frac{1}{8^{-3}}$

Combine terms. - $8 q^{4}-3 q^{4}$

Express the number in standard notation. - $7.3714 \times 10^{6}$

Add or subtract as indicated. - $\left(-3+2 x^{6}+7 x^{8}+8 x^{7}\right)+\left(-4 x^{7}+4 x^{6}+2+2 x^{8}\right)$

Choose the one alternative that best completes the statement or answers the question - $\frac{5^{-1}}{3^{-1}}$

Find the product - $(p+5 q)(p-5 q)$

Find the product - $(13 r-5)(13 r+5)$

Use scientific notation to simplify. Write the answer in both scientific notation and standard notation. - $\frac{49,000 \times 0.0004}{0.007 \times 7,000,000}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{19}}{x^{5}}$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $8^{-7}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 y^{2}-\frac{25}{3} y-3\right) \div(9 y+3)$

Evaluate the composition of functions. -Let $f(x)=x^{2}+2$ and $g(x)=3 x+6$ . Find $(g \circ f)(5)$ .

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-8 a^{3}$

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary. - $\mathrm{r}^{-3}$