Question 1

Give the domain and range of the function.
-$f(x)=\frac{1}{6} x^{2}$

Accepted Answer

A)  Domain: $\left(-\infty, \frac{1}{6}\right)$; range: $(-\infty, 0)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty, 0)$ 
C)  Domain: $(-\infty, \infty)$; range: $(0, \infty)$ 
D)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
A)  Domain: $\left(-\infty, \frac{1}{6}\right)$; range: $(-\infty, 0)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty, 0)$ 
C)  Domain: $(-\infty, \infty)$; range: $(0, \infty)$ 
D)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$

Question 2

Find the product
-$2 x(3 x-1)(3 x+7)$

Accepted Answer

A)  $14 x^{3}+38 x^{2}-12 x$ 
B)  $18 x^{3}+36 x^{2}-14 x$ 
C)  $16 x^{2}+37 x-14$ 
D)  $9 x^{3}+18 x^{2}-7 x$ 
A)  $14 x^{3}+38 x^{2}-12 x$ 
B)  $18 x^{3}+36 x^{2}-14 x$ 
C)  $16 x^{2}+37 x-14$ 
D)  $9 x^{3}+18 x^{2}-7 x$

Question 3

Choose the one alternative that best completes the statement or answers the question
-$7^{-1}-2^{-1}$

Accepted Answer

A)  $-\frac{1}{5}$ 
B)  $-\frac{14}{5}$ 
C)  $\frac{5}{14}$ 
D)  $-\frac{5}{14}$ 
A)  $-\frac{1}{5}$ 
B)  $-\frac{14}{5}$ 
C)  $\frac{5}{14}$ 
D)  $-\frac{5}{14}$

Question 4

$(9 m+11)^{2}$

Accepted Answer

A)  $81 m^{2}+121$ 
B)  $9 m^{2}+121$ 
C)  $81 m^{2}+198 m+121$ 
D)  $9 m^{2}+198 m+121$ 
A)  $81 m^{2}+121$ 
B)  $9 m^{2}+121$ 
C)  $81 m^{2}+198 m+121$ 
D)  $9 m^{2}+198 m+121$

Question 5

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

Accepted Answer

A)  $11 x^{4}-4 x^{3}+5 x^{2}+10$ 
B)  $-5 x^{4}-12 x^{3}-11 x^{2}+10$ 
C)  $11 x^{4}-4 x^{3}+5 x^{2}-6$ 
D)  $-5 x^{4}-4 x^{3}+5 x^{2}-6$ 
A)  $11 x^{4}-4 x^{3}+5 x^{2}+10$ 
B)  $-5 x^{4}-12 x^{3}-11 x^{2}+10$ 
C)  $11 x^{4}-4 x^{3}+5 x^{2}-6$ 
D)  $-5 x^{4}-4 x^{3}+5 x^{2}-6$

Question 6

Evaluate the expression.
-$-8^{0}$

Accepted Answer

A)  -8 
B)  0 
C)  1 
D)  -1 
A)  -8 
B)  0 
C)  1 
D)  -1

Question 7

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

Accepted Answer

A)  Monomial; -6 
B)  Binomial; 0 
C)  Binomial; 6 
D)  Binomial; 5 
A)  Monomial; -6 
B)  Binomial; 0 
C)  Binomial; 6 
D)  Binomial; 5

Question 8

Find the product
-$(n+12)^{2}$

Accepted Answer

A)  $n^{2}+24 n+144$ 
B)  $n^{2}+144$ 
C)  $n+144$ 
D)  $144 n^{2}+24 n+144$ 
A)  $n^{2}+24 n+144$ 
B)  $n^{2}+144$ 
C)  $n+144$ 
D)  $144 n^{2}+24 n+144$

Question 9

Write the polynomial in descending powers of the variable.
-$11-2 z^{2}+7 z-10 z^{3}$

Accepted Answer

A)  $10 z^{3}+2 z^{2}-7 z-11$ 
B)  $11+7 z-2 z^{2}-10 z^{3}$ 
C)  $-10 z^{3}-2 z^{2}+7 z+11$ 
D)  $11-10 z^{3}+7 z-2 z^{2}$ 
A)  $10 z^{3}+2 z^{2}-7 z-11$ 
B)  $11+7 z-2 z^{2}-10 z^{3}$ 
C)  $-10 z^{3}-2 z^{2}+7 z+11$ 
D)  $11-10 z^{3}+7 z-2 z^{2}$

Question 10

For the given pair of functions, find the requested function.
-$f(x)=4 x-4, g(x)=-7 x+6 ;(f-g)(x)$

Accepted Answer

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

Question 11

Apply the product rule for exponents, if possible.
-$x^{8} \cdot x^{6}$

Accepted Answer

A)  $x^{48}$ 
B)  $x^{14}$ 
C)  $x^{15}$ 
D)  $x^{12}$ 
A)  $x^{48}$ 
B)  $x^{14}$ 
C)  $x^{15}$ 
D)  $x^{12}$

Question 12

Add or subtract as indicated.
-$\left(6 x^{9}+11 x^{6}-8 x^{2}+8\right)-\left(9 x^{9}-5 x^{5}+4 x^{2}-12\right)$

Accepted Answer

A)  $3 x^{9}+11 x^{6}+5 x^{5}-12 x^{2}+20$ 
B)  $3 x^{9}+11 x^{6}-5 x^{5}-12 x^{2}+20$ 
C)  $-3 x^{9}+11 x^{6}+5 x^{5}-12 x^{2}+20$ 
D)  $-3 x^{9}+11 x^{6}-5 x^{5}-12 x^{2}+20$ 
A)  $3 x^{9}+11 x^{6}+5 x^{5}-12 x^{2}+20$ 
B)  $3 x^{9}+11 x^{6}-5 x^{5}-12 x^{2}+20$ 
C)  $-3 x^{9}+11 x^{6}+5 x^{5}-12 x^{2}+20$ 
D)  $-3 x^{9}+11 x^{6}-5 x^{5}-12 x^{2}+20$

Question 13

For the polynomial function, find the requested value.
-$f(x)=-2 x^{2}+7 x+8 ; f(-3)$

Accepted Answer

A)  -41 
B)  -7 
C)  -31 
D)  -35 
A)  -41 
B)  -7 
C)  -31 
D)  -35

Question 14

Choose the one alternative that best completes the statement or answers the question
-$3^{2}$

Accepted Answer

A)  $\frac{1}{9}$ 
B)  $\frac{1}{6}$ 
C)  6 
D)  9 
A)  $\frac{1}{9}$ 
B)  $\frac{1}{6}$ 
C)  6 
D)  9

Question 15

Evaluate the expression.
-$\frac{1}{-3^{-2}}$

Accepted Answer

A)  3 
B)  -3 
C)  -9 
D)  9 
A)  3 
B)  -3 
C)  -9 
D)  9

Question 16

Choose the one alternative that best completes the statement or answers the question
-$(-5)^{0}$

Accepted Answer

A)  0 
B)  1 
C)  -1 
D)  -5 
A)  0 
B)  1 
C)  -1 
D)  -5

Question 17

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\left(2 x^{2}+11 x+9\right) \div(9 x+9)$

Accepted Answer

A)  $x^{2}+99 x+1$ 
B)  $\frac{2}{9} x-1$ 
C)  $\frac{2}{9} x+1$ 
D)  $-7 x^{2}+20 x+9$ 
A)  $x^{2}+99 x+1$ 
B)  $\frac{2}{9} x-1$ 
C)  $\frac{2}{9} x+1$ 
D)  $-7 x^{2}+20 x+9$

Question 18

Write the number in standard form.
-$3.15 \times 10^{-4}$

Accepted Answer

A)  0.000315 
B)  0.00315 
C)  $-315,000$ 
D)  0.0000315 
A)  0.000315 
B)  0.00315 
C)  $-315,000$ 
D)  0.0000315

Question 19

Find the product
-$6 x^{3}\left(-8 x^{5}-11 x^{4}\right)$

Accepted Answer

A)  $-48 x^{8}-11 x^{4}$ 
B)  $-48 x^{8}-66 x^{7}$ 
C)  $-48 x^{8}+66 x^{7}$ 
D)  $-48 x^{15}-66 x^{12}$ 
A)  $-48 x^{8}-11 x^{4}$ 
B)  $-48 x^{8}-66 x^{7}$ 
C)  $-48 x^{8}+66 x^{7}$ 
D)  $-48 x^{15}-66 x^{12}$

Question 20

For the pair of functions, find the product $(f g)(x)$.
-$f(x)=5 x+4, g(x)=-x^{2}+6 x+7$

Accepted Answer

A)  $-5 x^{3}-27 x^{2}+59 x-28$ 
B)  $-10 x^{2}+26 x^{2}-59 x+28$ 
C)  $5 x^{3}+26 x^{2}-59 x-28$ 
D)  $-5 x^{3}+26 x^{2}+59 x+28$ 
A)  $-5 x^{3}-27 x^{2}+59 x-28$ 
B)  $-10 x^{2}+26 x^{2}-59 x+28$ 
C)  $5 x^{3}+26 x^{2}-59 x-28$ 
D)  $-5 x^{3}+26 x^{2}+59 x+28$

Give the domain and range of the function. - $f(x)=\frac{1}{6} x^{2}$

Find the product - $2 x(3 x-1)(3 x+7)$

Choose the one alternative that best completes the statement or answers the question - $7^{-1}-2^{-1}$

$(9 m+11)^{2}$

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

Evaluate the expression. - $-8^{0}$

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

Find the product - $(n+12)^{2}$

Write the polynomial in descending powers of the variable. - $11-2 z^{2}+7 z-10 z^{3}$

For the given pair of functions, find the requested function. - $f(x)=4 x-4, g(x)=-7 x+6 ;(f-g)(x)$

Apply the product rule for exponents, if possible. - $x^{8} \cdot x^{6}$

Add or subtract as indicated. - $\left(6 x^{9}+11 x^{6}-8 x^{2}+8\right)-\left(9 x^{9}-5 x^{5}+4 x^{2}-12\right)$

For the polynomial function, find the requested value. - $f(x)=-2 x^{2}+7 x+8 ; f(-3)$

Choose the one alternative that best completes the statement or answers the question - $3^{2}$

Evaluate the expression. - $\frac{1}{-3^{-2}}$

Choose the one alternative that best completes the statement or answers the question - $(-5)^{0}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 x^{2}+11 x+9\right) \div(9 x+9)$

Write the number in standard form. - $3.15 \times 10^{-4}$

Find the product - $6 x^{3}\left(-8 x^{5}-11 x^{4}\right)$

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+4, g(x)=-x^{2}+6 x+7$

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

Give the domain and range of the function. - f(x)=16x2f(x)=\frac{1}{6} x^{2}f(x)=61​x2

Find the product - 2x(3x−1)(3x+7)2 x(3 x-1)(3 x+7)2x(3x−1)(3x+7)

Choose the one alternative that best completes the statement or answers the question - 7−1−2−17^{-1}-2^{-1}7−1−2−1

(9m+11)2(9 m+11)^{2}(9m+11)2

Add or subtract as indicated. - (−3x2+3x4+2−8x3)−(−8+4x3+8x4+8x2)\left(-3 x^{2}+3 x^{4}+2-8 x^{3}\right)-\left(-8+4 x^{3}+8 x^{4}+8 x^{2}\right)(−3x2+3x4+2−8x3)−(−8+4x3+8x4+8x2)

Evaluate the expression. - −80-8^{0}−80

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - −6y5−4-6 y^{5}-4−6y5−4

Find the product - (n+12)2(n+12)^{2}(n+12)2

Write the polynomial in descending powers of the variable. - 11−2z2+7z−10z311-2 z^{2}+7 z-10 z^{3}11−2z2+7z−10z3

For the given pair of functions, find the requested function. - f(x)=4x−4,g(x)=−7x+6;(f−g)(x)f(x)=4 x-4, g(x)=-7 x+6 ;(f-g)(x)f(x)=4x−4,g(x)=−7x+6;(f−g)(x)

Apply the product rule for exponents, if possible. - x8⋅x6x^{8} \cdot x^{6}x8⋅x6

Add or subtract as indicated. - (6x9+11x6−8x2+8)−(9x9−5x5+4x2−12)\left(6 x^{9}+11 x^{6}-8 x^{2}+8\right)-\left(9 x^{9}-5 x^{5}+4 x^{2}-12\right)(6x9+11x6−8x2+8)−(9x9−5x5+4x2−12)

For the polynomial function, find the requested value. - f(x)=−2x2+7x+8;f(−3)f(x)=-2 x^{2}+7 x+8 ; f(-3)f(x)=−2x2+7x+8;f(−3)

Choose the one alternative that best completes the statement or answers the question - 323^{2}32

Evaluate the expression. - 1−3−2\frac{1}{-3^{-2}}−3−21​

Choose the one alternative that best completes the statement or answers the question - (−5)0(-5)^{0}(−5)0

Choose the one alternative that best completes the statement or answers the question. Divide - (2x2+11x+9)÷(9x+9)\left(2 x^{2}+11 x+9\right) \div(9 x+9)(2x2+11x+9)÷(9x+9)

Write the number in standard form. - 3.15×10−43.15 \times 10^{-4}3.15×10−4

Find the product - 6x3(−8x5−11x4)6 x^{3}\left(-8 x^{5}-11 x^{4}\right)6x3(−8x5−11x4)

For the pair of functions, find the product (fg)(x)(f g)(x)(fg)(x) . - f(x)=5x+4,g(x)=−x2+6x+7f(x)=5 x+4, g(x)=-x^{2}+6 x+7f(x)=5x+4,g(x)=−x2+6x+7

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

Give the domain and range of the function. - $f(x)=\frac{1}{6} x^{2}$

Find the product - $2 x(3 x-1)(3 x+7)$

Choose the one alternative that best completes the statement or answers the question - $7^{-1}-2^{-1}$

$(9 m+11)^{2}$

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

Evaluate the expression. - $-8^{0}$

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

Find the product - $(n+12)^{2}$

Write the polynomial in descending powers of the variable. - $11-2 z^{2}+7 z-10 z^{3}$

For the given pair of functions, find the requested function. - $f(x)=4 x-4, g(x)=-7 x+6 ;(f-g)(x)$

Apply the product rule for exponents, if possible. - $x^{8} \cdot x^{6}$

Add or subtract as indicated. - $\left(6 x^{9}+11 x^{6}-8 x^{2}+8\right)-\left(9 x^{9}-5 x^{5}+4 x^{2}-12\right)$

For the polynomial function, find the requested value. - $f(x)=-2 x^{2}+7 x+8 ; f(-3)$

Choose the one alternative that best completes the statement or answers the question - $3^{2}$

Evaluate the expression. - $\frac{1}{-3^{-2}}$

Choose the one alternative that best completes the statement or answers the question - $(-5)^{0}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(2 x^{2}+11 x+9\right) \div(9 x+9)$

Write the number in standard form. - $3.15 \times 10^{-4}$

Find the product - $6 x^{3}\left(-8 x^{5}-11 x^{4}\right)$

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+4, g(x)=-x^{2}+6 x+7$