Question 1

$[(5 x-2)+4 y]^{2}$

Accepted Answer

A)  $25 x^{2}-10 x+4+20 x y+8 y+16 y^{2}$ 
B)  $25 x^{2}-20 x+40 x y-16 y+16 y^{2}$ 
C)  $25 x^{2}-20 x+4+20 x y+8 y+16 y^{2}$ 
D)  $25 x^{2}-20 x+4+40 x y-16 y+16 y^{2}$ 
A)  $25 x^{2}-10 x+4+20 x y+8 y+16 y^{2}$ 
B)  $25 x^{2}-20 x+40 x y-16 y+16 y^{2}$ 
C)  $25 x^{2}-20 x+4+20 x y+8 y+16 y^{2}$ 
D)  $25 x^{2}-20 x+4+40 x y-16 y+16 y^{2}$ D

Question 2

For the polynomial function, find the requested value.
-$f(x)=-7 x+6 ; f(2)$

Accepted Answer

A)  -1 
B)  -28 
C)  -8 
D)  -20 
A)  -1 
B)  -28 
C)  -8 
D)  -20 C

Question 3

Express the number in standard notation.
-$4.0813 \times 10^{-7}$

Accepted Answer

A)  0.000000040813 
B)  $-408,130,000$ 
C)  0.0000040813 
D)  0.00000040813 
A)  0.000000040813 
B)  $-408,130,000$ 
C)  0.0000040813 
D)  0.00000040813 D

Question 4

Give the numerical coefficient and the degree of the term.
-$-11 \mathrm{z}^{3}$

Accepted Answer

A)  Coefficient: -11; degree: 3 
B)  Coefficient: 3; degree: 11 
C)  Coefficient: 11; degree: 3 
D)  Coefficient: 1; degree: 11 
A)  Coefficient: -11; degree: 3 
B)  Coefficient: 3; degree: 11 
C)  Coefficient: 11; degree: 3 
D)  Coefficient: 1; degree: 11

Question 5

Find the value of the expression.
-$\frac{16,000 \times 0.09}{36,000}$

Accepted Answer

A)  0.04 
B)  40,000 
C)  0.4 
D)  0.004 
A)  0.04 
B)  40,000 
C)  0.4 
D)  0.004

Question 6

Explain how to find the product of two monomials by using the following example: $9 n^{5} x^{6} y^{3} \cdot-2 n^{2} x y^{4}$

Accepted Answer

Answers will vary, but should

Question 7

$(-3 x-5)^{2}$

Accepted Answer

A)  $9 x^{2}+30 x+25$ 
B)  $-3 x^{2}+30 x+25$ 
C)  $9 x^{2}+25$ 
D)  $-3 x^{2}+25$ 
A)  $9 x^{2}+30 x+25$ 
B)  $-3 x^{2}+30 x+25$ 
C)  $9 x^{2}+25$ 
D)  $-3 x^{2}+25$

Question 8

Write the polynomial in descending powers of the variable.
-$4 x-2 x^{3}+5 x^{2}$

Accepted Answer

A)  $4 x+5 x^{2}-2 x^{3}$ 
B)  $5 x^{2}-2 x^{3}+4 x$ 
C)  $5 x^{2}+4 x-2 x^{3}$ 
D)  $-2 x^{3}+5 x^{2}+4 x$ 
A)  $4 x+5 x^{2}-2 x^{3}$ 
B)  $5 x^{2}-2 x^{3}+4 x$ 
C)  $5 x^{2}+4 x-2 x^{3}$ 
D)  $-2 x^{3}+5 x^{2}+4 x$

Question 9

For the given pair of functions, find the requested function.
-If $f(x)=x^{2}+11 x+24$ and $g(x)=x+3$, find $\left(\frac{f}{g}\right)(x)$.

Accepted Answer

A)  $x^{3}-21$ 
B)  $x+8$ 
C)  $x-21$ 
D)  $x^{2}+8$ 
A)  $x^{3}-21$ 
B)  $x+8$ 
C)  $x-21$ 
D)  $x^{2}+8$

Question 10

For the polynomial function, find the requested value.
-$f(x)=-4 x^{5}-6 x^{4}+6 x^{3}-x^{2} ; f(-2)$

Accepted Answer

A)  -25 
B)  -24 
C)  9 
D)  -20 
A)  -25 
B)  -24 
C)  9 
D)  -20

Question 11

A rectangular patio has an area of $4 m^{3}+24 m^{2}+8 m-48$. Find the length if the width is $4 m+8$.

Accepted Answer

A)  $m^{3}+4 m^{2}-6 m$ 
B)  $m^{2}+16 m-6$ 
C)  $m^{2}-4 m+6$ 
D)  $m^{2}+4 m-6$ 
A)  $m^{3}+4 m^{2}-6 m$ 
B)  $m^{2}+16 m-6$ 
C)  $m^{2}-4 m+6$ 
D)  $m^{2}+4 m-6$

Question 12

$f(x)=2 x^{2}+7 x+12$ and $g(x)=13 x^{2}+16 x-6 ;(f-g)(x)$

Accepted Answer

A)  $-11 x^{2}-9 x+18$ 
B)  $-11 x^{4}-9 x^{2}+18$ 
C)  $-11 x^{2}-9 x+6$ 
D)  $-11 x^{2}+9 x-18$ 
A)  $-11 x^{2}-9 x+18$ 
B)  $-11 x^{4}-9 x^{2}+18$ 
C)  $-11 x^{2}-9 x+6$ 
D)  $-11 x^{2}+9 x-18$

Question 13

Apply the product rule for exponents, if possible.
-$y^{3} \cdot y^{6} \cdot y^{2}$

Accepted Answer

A)  $y^{36}$ 
B)  $y^{13}$ 
C)  $y^{9}$ 
D)  $y^{11}$ 
A)  $y^{36}$ 
B)  $y^{13}$ 
C)  $y^{9}$ 
D)  $y^{11}$

Question 14

Find the product
-$\left(4 x^{3}-x^{2}+4 x-1\right)(2 x+2)$

Accepted Answer

A)  $8 x^{4}+6 x^{3}+6 x^{2}+6 x-2$ 
B)  $8 x^{3}+6 x^{2}+6 x+6$ 
C)  $9 x^{4}-6 x^{3}+5 x^{2}-6 x+2$ 
D)  $7 x^{4}+10 x^{3}+8 x^{2}+8 x-4$ 
A)  $8 x^{4}+6 x^{3}+6 x^{2}+6 x-2$ 
B)  $8 x^{3}+6 x^{2}+6 x+6$ 
C)  $9 x^{4}-6 x^{3}+5 x^{2}-6 x+2$ 
D)  $7 x^{4}+10 x^{3}+8 x^{2}+8 x-4$

Question 15

Give the numerical coefficient and the degree of the term.
-$5 \mathrm{a}^{4} \mathrm{~b}^{2}$

Accepted Answer

A)  Coefficient: 5 ; degree: 6 
B)  Coefficient: 5; degree: 4 
C)  Coefficient: 1 ; degree: 6 
D)  Coefficient: 1; degree: 7 
A)  Coefficient: 5 ; degree: 6 
B)  Coefficient: 5; degree: 4 
C)  Coefficient: 1 ; degree: 6 
D)  Coefficient: 1; degree: 7

Question 16

Explain how to find the product of two polynomials by using the following example: $(4 q+4)\left(5 q^{2}-8 q-8\right)$

Accepted Answer

Answers will vary, but should

Question 17

Give the domain and range of the function.
-$f(x)=15 x$

Accepted Answer

A)  Domain: $(-\infty, 15)$; range: $(-15, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
C)  Domain: $(-15,15)$; range: $(-\infty, \infty)$ 
D)  Domain: $(-\infty,-15)$; range: $(-\infty, \infty)$ 
A)  Domain: $(-\infty, 15)$; range: $(-15, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
C)  Domain: $(-15,15)$; range: $(-\infty, \infty)$ 
D)  Domain: $(-\infty,-15)$; range: $(-\infty, \infty)$

Question 18

$[(7 x+3)+2 y]^{2}$

Accepted Answer

A)  $49 x^{2}+28 x y+4 y^{2}$ 
B)  $49 x^{2}+42 x+28 x y+12 y+4 y^{2}$ 
C)  $49 x^{2}+42 x+9+28 x y+12 y+4 y^{2}$ 
D)  $49 x^{2}+21 x+9+14 x y+6 y+4 y^{2}$ 
A)  $49 x^{2}+28 x y+4 y^{2}$ 
B)  $49 x^{2}+42 x+28 x y+12 y+4 y^{2}$ 
C)  $49 x^{2}+42 x+9+28 x y+12 y+4 y^{2}$ 
D)  $49 x^{2}+21 x+9+14 x y+6 y+4 y^{2}$

Question 19

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{y^{2}+10 y+25}{y+5}$

Accepted Answer

A)  $y+\frac{5}{y+5}$ 
B)  $y^{2}+5$ 
C)  $y-5$ 
D)  $y+5$ 
A)  $y+\frac{5}{y+5}$ 
B)  $y^{2}+5$ 
C)  $y-5$ 
D)  $y+5$

Question 20

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
-$\frac{\left(3 x^{4} y^{2}\right)^{6}}{9 x y^{2}}$

Accepted Answer

A)  $\frac{x^{9} y^{6}}{3}$ 
B)  $\frac{x^{23} y^{10}}{3}$ 
C)  $81 x^{23} y^{10}$ 
D)  $81 x^{9} y^{6}$ 
A)  $\frac{x^{9} y^{6}}{3}$ 
B)  $\frac{x^{23} y^{10}}{3}$ 
C)  $81 x^{23} y^{10}$ 
D)  $81 x^{9} y^{6}$

$[(5 x-2)+4 y]^{2}$

For the polynomial function, find the requested value. - $f(x)=-7 x+6 ; f(2)$

Express the number in standard notation. - $4.0813 \times 10^{-7}$

Give the numerical coefficient and the degree of the term. - $-11 \mathrm{z}^{3}$

Find the value of the expression. - $\frac{16,000 \times 0.09}{36,000}$

Explain how to find the product of two monomials by using the following example: $9 n^{5} x^{6} y^{3} \cdot-2 n^{2} x y^{4}$

$(-3 x-5)^{2}$

Write the polynomial in descending powers of the variable. - $4 x-2 x^{3}+5 x^{2}$

For the given pair of functions, find the requested function. -If $f(x)=x^{2}+11 x+24$ and $g(x)=x+3$ , find $\left(\frac{f}{g}\right)(x)$ .

For the polynomial function, find the requested value. - $f(x)=-4 x^{5}-6 x^{4}+6 x^{3}-x^{2} ; f(-2)$

A rectangular patio has an area of $4 m^{3}+24 m^{2}+8 m-48$ . Find the length if the width is $4 m+8$ .

$f(x)=2 x^{2}+7 x+12$ and $g(x)=13 x^{2}+16 x-6 ;(f-g)(x)$

Apply the product rule for exponents, if possible. - $y^{3} \cdot y^{6} \cdot y^{2}$

Find the product - $\left(4 x^{3}-x^{2}+4 x-1\right)(2 x+2)$

Give the numerical coefficient and the degree of the term. - $5 \mathrm{a}^{4} \mathrm{~b}^{2}$

Explain how to find the product of two polynomials by using the following example: $(4 q+4)\left(5 q^{2}-8 q-8\right)$

Give the domain and range of the function. - $f(x)=15 x$

$[(7 x+3)+2 y]^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{y^{2}+10 y+25}{y+5}$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\frac{\left(3 x^{4} y^{2}\right)^{6}}{9 x y^{2}}$

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

[(5x−2)+4y]2[(5 x-2)+4 y]^{2}[(5x−2)+4y]2

For the polynomial function, find the requested value. - f(x)=−7x+6;f(2)f(x)=-7 x+6 ; f(2)f(x)=−7x+6;f(2)

Express the number in standard notation. - 4.0813×10−74.0813 \times 10^{-7}4.0813×10−7

Give the numerical coefficient and the degree of the term. - −11z3-11 \mathrm{z}^{3}−11z3

Find the value of the expression. - 16,000×0.0936,000\frac{16,000 \times 0.09}{36,000}36,00016,000×0.09​

Explain how to find the product of two monomials by using the following example: 9n5x6y3⋅−2n2xy49 n^{5} x^{6} y^{3} \cdot-2 n^{2} x y^{4}9n5x6y3⋅−2n2xy4

(−3x−5)2(-3 x-5)^{2}(−3x−5)2

Write the polynomial in descending powers of the variable. - 4x−2x3+5x24 x-2 x^{3}+5 x^{2}4x−2x3+5x2

For the given pair of functions, find the requested function. -If f(x)=x2+11x+24f(x)=x^{2}+11 x+24f(x)=x2+11x+24 and g(x)=x+3g(x)=x+3g(x)=x+3 , find (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) .

For the polynomial function, find the requested value. - f(x)=−4x5−6x4+6x3−x2;f(−2)f(x)=-4 x^{5}-6 x^{4}+6 x^{3}-x^{2} ; f(-2)f(x)=−4x5−6x4+6x3−x2;f(−2)

A rectangular patio has an area of 4m3+24m2+8m−484 m^{3}+24 m^{2}+8 m-484m3+24m2+8m−48 . Find the length if the width is 4m+84 m+84m+8 .

f(x)=2x2+7x+12f(x)=2 x^{2}+7 x+12f(x)=2x2+7x+12 and g(x)=13x2+16x−6;(f−g)(x)g(x)=13 x^{2}+16 x-6 ;(f-g)(x)g(x)=13x2+16x−6;(f−g)(x)

Apply the product rule for exponents, if possible. - y3⋅y6⋅y2y^{3} \cdot y^{6} \cdot y^{2}y3⋅y6⋅y2

Find the product - (4x3−x2+4x−1)(2x+2)\left(4 x^{3}-x^{2}+4 x-1\right)(2 x+2)(4x3−x2+4x−1)(2x+2)

Give the numerical coefficient and the degree of the term. - 5a4 b25 \mathrm{a}^{4} \mathrm{~b}^{2}5a4 b2

Explain how to find the product of two polynomials by using the following example: (4q+4)(5q2−8q−8)(4 q+4)\left(5 q^{2}-8 q-8\right)(4q+4)(5q2−8q−8)

Give the domain and range of the function. - f(x)=15xf(x)=15 xf(x)=15x

[(7x+3)+2y]2[(7 x+3)+2 y]^{2}[(7x+3)+2y]2

Choose the one alternative that best completes the statement or answers the question. Divide - y2+10y+25y+5\frac{y^{2}+10 y+25}{y+5}y+5y2+10y+25​

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - (3x4y2)69xy2\frac{\left(3 x^{4} y^{2}\right)^{6}}{9 x y^{2}}9xy2(3x4y2)6​

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

$[(5 x-2)+4 y]^{2}$

For the polynomial function, find the requested value. - $f(x)=-7 x+6 ; f(2)$

Express the number in standard notation. - $4.0813 \times 10^{-7}$

Give the numerical coefficient and the degree of the term. - $-11 \mathrm{z}^{3}$

Find the value of the expression. - $\frac{16,000 \times 0.09}{36,000}$

Explain how to find the product of two monomials by using the following example: $9 n^{5} x^{6} y^{3} \cdot-2 n^{2} x y^{4}$

$(-3 x-5)^{2}$

Write the polynomial in descending powers of the variable. - $4 x-2 x^{3}+5 x^{2}$

For the given pair of functions, find the requested function. -If $f(x)=x^{2}+11 x+24$ and $g(x)=x+3$ , find $\left(\frac{f}{g}\right)(x)$ .

For the polynomial function, find the requested value. - $f(x)=-4 x^{5}-6 x^{4}+6 x^{3}-x^{2} ; f(-2)$

A rectangular patio has an area of $4 m^{3}+24 m^{2}+8 m-48$ . Find the length if the width is $4 m+8$ .

$f(x)=2 x^{2}+7 x+12$ and $g(x)=13 x^{2}+16 x-6 ;(f-g)(x)$

Apply the product rule for exponents, if possible. - $y^{3} \cdot y^{6} \cdot y^{2}$

Find the product - $\left(4 x^{3}-x^{2}+4 x-1\right)(2 x+2)$

Give the numerical coefficient and the degree of the term. - $5 \mathrm{a}^{4} \mathrm{~b}^{2}$

Explain how to find the product of two polynomials by using the following example: $(4 q+4)\left(5 q^{2}-8 q-8\right)$

Give the domain and range of the function. - $f(x)=15 x$

$[(7 x+3)+2 y]^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{y^{2}+10 y+25}{y+5}$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\frac{\left(3 x^{4} y^{2}\right)^{6}}{9 x y^{2}}$