A) $5 a^{2}+81$ B) $5 a^{2}-90 a+81$ C) $25 a^{2}+81$ D) $25 a^{2}-90 a+81$ A) $5 a^{2}+81$ B) $5 a^{2}-90 a+81$ C) $25 a^{2}+81$ D) $25 a^{2}-90 a+81$

Exam 5: Exponents, Polynomials, and Polynomial Functions

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. - $f(x)=15 x^{2}-3 x, g(x)=3 x$

(Multiple Choice)

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Question 281

The volume of a box is $3 p^{4}+27 p^{3}+42 p^{2}$ . The height is $p$ , and the width is $p+7$ . What is the length?

(Multiple Choice)

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Question 282

Find the value of the expression. - $\frac{18 \times 10^{8}}{6 \times 10^{6}}$

(Multiple Choice)

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Question 283

Graph the function. - $f(x)=x^{2}-4$ $Graph the function. - f(x)=x^{2}-4$

(Multiple Choice)

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Question 284

Evaluate the expression. - $(-11)^{0}+(-7)^{0}$

(Multiple Choice)

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Question 285

For the given pair of functions, find the requested function. - $f(x)=5 x-3, g(x)=-9 x^{2}-15 x+6 ;(f+g)(x)$

(Multiple Choice)

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Question 286

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}$

(Multiple Choice)

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Question 287

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

(Multiple Choice)

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Question 288

Give the domain and range of the function. - $f(x)=-\frac{1}{2} x^{2}$

(Multiple Choice)

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Question 289

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 x^{2}-\frac{95}{9} x+7\right) \div(9 x-7)$

(Multiple Choice)

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Question 290

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

(Multiple Choice)

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Question 291

Given that $0 < x <1$ and $x^{n}=y$ , explain why as $n$ becomes larger, $y$ becomes closer to 0 .

(Essay)

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Question 292

Find the product - $[(3 x-y)+2 z][(3 x-y)-2 z]$

(Multiple Choice)

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Question 293

Find the requested value. -If $f(x)=4 x+2$ and $g(x)=8 x^{2}-7 x+1$ , find $(f g)(x)$ .

(Multiple Choice)

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Question 294

The function $f(x)=60 x$ computes the number of minutes in $x$ hours. The function $g(x)=24 x$ computes the number of hours in $x$ days. What is $(f \circ g)(x)$ and what does it compute?

(Multiple Choice)

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Question 295

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+3, g(x)=4 x-8$

(Multiple Choice)

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Question 296

$(5 a-9)^{2}$

(Multiple Choice)

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Question 297

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{2 r^{3}-4 r^{2}-8 r-32}{2 r^{2}+4 r+8}$

(Multiple Choice)

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Question 298

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{5}}{y^{9}}$

(Multiple Choice)

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Question 299

Evaluate the expression. - $\left(\frac{2}{7}\right)^{-4}$

(Multiple Choice)

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Question 300

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. - $f(x)=15 x^{2}-3 x, g(x)=3 x$

The volume of a box is $3 p^{4}+27 p^{3}+42 p^{2}$ . The height is $p$ , and the width is $p+7$ . What is the length?

Find the value of the expression. - $\frac{18 \times 10^{8}}{6 \times 10^{6}}$

Graph the function. - $f(x)=x^{2}-4$ $Graph the function. - f(x)=x^{2}-4$

Evaluate the expression. - $(-11)^{0}+(-7)^{0}$

For the given pair of functions, find the requested function. - $f(x)=5 x-3, g(x)=-9 x^{2}-15 x+6 ;(f+g)(x)$

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}$

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

Give the domain and range of the function. - $f(x)=-\frac{1}{2} x^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 x^{2}-\frac{95}{9} x+7\right) \div(9 x-7)$

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

Given that $0 < x <1$ and $x^{n}=y$ , explain why as $n$ becomes larger, $y$ becomes closer to 0 .

Find the product - $[(3 x-y)+2 z][(3 x-y)-2 z]$

Find the requested value. -If $f(x)=4 x+2$ and $g(x)=8 x^{2}-7 x+1$ , find $(f g)(x)$ .

The function $f(x)=60 x$ computes the number of minutes in $x$ hours. The function $g(x)=24 x$ computes the number of hours in $x$ days. What is $(f \circ g)(x)$ and what does it compute?

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+3, g(x)=4 x-8$

$(5 a-9)^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{2 r^{3}-4 r^{2}-8 r-32}{2 r^{2}+4 r+8}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{5}}{y^{9}}$

Evaluate the expression. - $\left(\frac{2}{7}\right)^{-4}$

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

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Exam 5: Exponents, Polynomials, and Polynomial Functions

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)=15x2−3x,g(x)=3xf(x)=15 x^{2}-3 x, g(x)=3 xf(x)=15x2−3x,g(x)=3x

The volume of a box is 3p4+27p3+42p23 p^{4}+27 p^{3}+42 p^{2}3p4+27p3+42p2 . The height is ppp , and the width is p+7p+7p+7 . What is the length?

Find the value of the expression. - 18×1086×106\frac{18 \times 10^{8}}{6 \times 10^{6}}6×10618×108​

Graph the function. - f(x)=x2−4f(x)=x^{2}-4f(x)=x2−4

Evaluate the expression. - (−11)0+(−7)0(-11)^{0}+(-7)^{0}(−11)0+(−7)0

For the given pair of functions, find the requested function. - f(x)=5x−3,g(x)=−9x2−15x+6;(f+g)(x)f(x)=5 x-3, g(x)=-9 x^{2}-15 x+6 ;(f+g)(x)f(x)=5x−3,g(x)=−9x2−15x+6;(f+g)(x)

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - (2x2y5)−1(3x2y3)3\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}(3x2y3)3(2x2y5)−1​

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

Give the domain and range of the function. - f(x)=−12x2f(x)=-\frac{1}{2} x^{2}f(x)=−21​x2

Choose the one alternative that best completes the statement or answers the question. Divide - (2x2−959x+7)÷(9x−7)\left(2 x^{2}-\frac{95}{9} x+7\right) \div(9 x-7)(2x2−995​x+7)÷(9x−7)

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

Given that 0<x<10 < x <10<x<1 and xn=yx^{n}=yxn=y , explain why as nnn becomes larger, yyy becomes closer to 0 .

Find the product - [(3x−y)+2z][(3x−y)−2z][(3 x-y)+2 z][(3 x-y)-2 z][(3x−y)+2z][(3x−y)−2z]

Find the requested value. -If f(x)=4x+2f(x)=4 x+2f(x)=4x+2 and g(x)=8x2−7x+1g(x)=8 x^{2}-7 x+1g(x)=8x2−7x+1 , find (fg)(x)(f g)(x)(fg)(x) .

The function f(x)=60xf(x)=60 xf(x)=60x computes the number of minutes in xxx hours. The function g(x)=24xg(x)=24 xg(x)=24x computes the number of hours in xxx days. What is (f∘g)(x)(f \circ g)(x)(f∘g)(x) and what does it compute?

For the pair of functions, find the product (fg)(x)(f g)(x)(fg)(x) . - f(x)=5x+3,g(x)=4x−8f(x)=5 x+3, g(x)=4 x-8f(x)=5x+3,g(x)=4x−8

(5a−9)2(5 a-9)^{2}(5a−9)2

Choose the one alternative that best completes the statement or answers the question. Divide - 2r3−4r2−8r−322r2+4r+8\frac{2 r^{3}-4 r^{2}-8 r-32}{2 r^{2}+4 r+8}2r2+4r+82r3−4r2−8r−32​

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - x5y9\frac{x^{5}}{y^{9}}y9x5​

Evaluate the expression. - (27)−4\left(\frac{2}{7}\right)^{-4}(72​)−4

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 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. - $f(x)=15 x^{2}-3 x, g(x)=3 x$

The volume of a box is $3 p^{4}+27 p^{3}+42 p^{2}$ . The height is $p$ , and the width is $p+7$ . What is the length?

Find the value of the expression. - $\frac{18 \times 10^{8}}{6 \times 10^{6}}$

Graph the function. - $f(x)=x^{2}-4$ $Graph the function. - f(x)=x^{2}-4$

Evaluate the expression. - $(-11)^{0}+(-7)^{0}$

For the given pair of functions, find the requested function. - $f(x)=5 x-3, g(x)=-9 x^{2}-15 x+6 ;(f+g)(x)$

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}$

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

Give the domain and range of the function. - $f(x)=-\frac{1}{2} x^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 x^{2}-\frac{95}{9} x+7\right) \div(9 x-7)$

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

Given that $0 < x <1$ and $x^{n}=y$ , explain why as $n$ becomes larger, $y$ becomes closer to 0 .

Find the product - $[(3 x-y)+2 z][(3 x-y)-2 z]$

Find the requested value. -If $f(x)=4 x+2$ and $g(x)=8 x^{2}-7 x+1$ , find $(f g)(x)$ .

The function $f(x)=60 x$ computes the number of minutes in $x$ hours. The function $g(x)=24 x$ computes the number of hours in $x$ days. What is $(f \circ g)(x)$ and what does it compute?

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+3, g(x)=4 x-8$

$(5 a-9)^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{2 r^{3}-4 r^{2}-8 r-32}{2 r^{2}+4 r+8}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{5}}{y^{9}}$

Evaluate the expression. - $\left(\frac{2}{7}\right)^{-4}$