Question 1

Add or subtract as indicated.
-$\left(-6 x^{6}+8 x^{8}+4-8 x^{7}\right)-\left(6+5 x^{7}+5 x^{8}+8 x^{6}\right)$

Accepted Answer

A)  $3 x^{8}-13 x^{7}-14 x^{6}-2$ 
B)  $13 x^{8}-3 x^{7}+2 x^{6}-2$ 
C)  $13 x^{8}-3 x^{7}+2 x^{6}+10$ 
D)  $3 x^{8}-3 x^{7}+2 x^{6}+10$ 
A)  $3 x^{8}-13 x^{7}-14 x^{6}-2$ 
B)  $13 x^{8}-3 x^{7}+2 x^{6}-2$ 
C)  $13 x^{8}-3 x^{7}+2 x^{6}+10$ 
D)  $3 x^{8}-3 x^{7}+2 x^{6}+10$

Question 2

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(\frac{-3 w^{5}}{x}\right)^{4}$

Accepted Answer

A)  $\frac{81 w^{9}}{x^{4}}$ 
B)  $\frac{-81 w^{20}}{x^{4}}$ 
C)  $\frac{-81 w^{20}}{x}$ 
D)  $\frac{81 w^{20}}{x^{4}}$ 
A)  $\frac{81 w^{9}}{x^{4}}$ 
B)  $\frac{-81 w^{20}}{x^{4}}$ 
C)  $\frac{-81 w^{20}}{x}$ 
D)  $\frac{81 w^{20}}{x^{4}}$

Question 3

Express the number in scientific notation
-0.000000034603

Accepted Answer

A)  $3.4603 \times 10^{-9}$ 
B)  $3.4603 \times 10^{-8}$ 
C)  $3.4603 \times 10^{-7}$ 
D)  $3.4603 \times 10^{8}$ 
A)  $3.4603 \times 10^{-9}$ 
B)  $3.4603 \times 10^{-8}$ 
C)  $3.4603 \times 10^{-7}$ 
D)  $3.4603 \times 10^{8}$

Question 4

Find the product
-$(-9+x)(4 x-4)$

Accepted Answer

A)  $4 x^{2}-41 x+36$ 
B)  $4 x^{2}-40 x+36$ 
C)  $x^{2}-40 x-40$ 
D)  $4 x^{2}+36 x-40$ 
A)  $4 x^{2}-41 x+36$ 
B)  $4 x^{2}-40 x+36$ 
C)  $x^{2}-40 x-40$ 
D)  $4 x^{2}+36 x-40$

Question 5

Find the requested value.
-If $f(x)=2 x+2$ and $g(x)=8 x^{2}-9 x+5$, find (fg) $(-5)$.

Accepted Answer

A)  -2010 
B)  -2000 
C)  -1900 
D)  502 
A)  -2010 
B)  -2000 
C)  -1900 
D)  502

Question 6

$(\mathrm{w}-13)^{2}$

Accepted Answer

A)  $w^{2}-26 w+169$ 
B)  $w+169$ 
C)  $169 w^{2}-26 w+169$ 
D)  $\mathrm{w}^{2}+169$ 
A)  $w^{2}-26 w+169$ 
B)  $w+169$ 
C)  $169 w^{2}-26 w+169$ 
D)  $\mathrm{w}^{2}+169$

Question 7

Find the product
-$(a-11)(a+11)$

Accepted Answer

A)  $a^{2}-22 a-121$ 
B)  $a^{2}+22 a-121$ 
C)  $a^{2}-121$ 
D)  $a^{2}-22$ 
A)  $a^{2}-22 a-121$ 
B)  $a^{2}+22 a-121$ 
C)  $a^{2}-121$ 
D)  $a^{2}-22$

Question 8

Decide whether the expression has been simplified correctly.
-$(2 b)^{4}=2^{4} b^{4}$

Accepted Answer

A) True 
 B)False

Question 9

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{x^{2}+11 x+18}{x+2}$

Accepted Answer

A)  $x^{2}+9$ 
B)  $x+9$ 
C)  $x-16$ 
D)  $x^{3}-16$ 
A)  $x^{2}+9$ 
B)  $x+9$ 
C)  $x-16$ 
D)  $x^{3}-16$

Question 10

Find the product
-$\left(-2 x^{2}-10 y\right)\left(-4 x^{2}-12 y+z\right)$

Accepted Answer

A)  $8 x^{4}+64 x^{2} y^{2}+120 y^{2}$ 
B)  $8 x^{2}+64 x y-2 x^{2} z+120 y^{2}-10 z$ 
C)  $8 x^{4}+64 x^{2} y+120 y^{4}-2 x^{2} y z$ 
D)  $8 x^{4}+64 x^{2} y-2 x^{2} z+120 y^{2}-10 y z$ 
A)  $8 x^{4}+64 x^{2} y^{2}+120 y^{2}$ 
B)  $8 x^{2}+64 x y-2 x^{2} z+120 y^{2}-10 z$ 
C)  $8 x^{4}+64 x^{2} y+120 y^{4}-2 x^{2} y z$ 
D)  $8 x^{4}+64 x^{2} y-2 x^{2} z+120 y^{2}-10 y z$

Question 11

Find the product
-$(m+6)(m-6)$

Accepted Answer

A)  $m^{2}-12$ 
B)  $m^{2}-12 m-36$ 
C)  $m^{2}-12 m+36$ 
D)  $m^{2}-36$ 
A)  $m^{2}-12$ 
B)  $m^{2}-12 m-36$ 
C)  $m^{2}-12 m+36$ 
D)  $m^{2}-36$

Question 12

For the pair of functions, find the product $(f g)(x)$.
-$f(x)=5 x+3, g(x)=-4 x-7$

Accepted Answer

A)  $-21 x^{2}-49 x-23$ 
B)  $-18 x^{2}+47 x-21$ 
C)  $-20 x^{2}-47 x-21$ 
D)  $20 x^{2}+47 x-21$ 
A)  $-21 x^{2}-49 x-23$ 
B)  $-18 x^{2}+47 x-21$ 
C)  $-20 x^{2}-47 x-21$ 
D)  $20 x^{2}+47 x-21$

Question 13

Give the domain and range of the function.
-$f(x)=x^{3}+5$

Accepted Answer

A)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
B)  Domain: $(-5, \infty)$; range: $(-\infty, 5)$ 
C)  Domain: $(-\infty, \infty)$; range: $(-\infty, 0)$ 
D)  Domain: $(0, \infty)$; range: $(-\infty, \infty)$ 
A)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
B)  Domain: $(-5, \infty)$; range: $(-\infty, 5)$ 
C)  Domain: $(-\infty, \infty)$; range: $(-\infty, 0)$ 
D)  Domain: $(0, \infty)$; range: $(-\infty, \infty)$

Question 14

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

Accepted Answer

A)  $5 x^{2}+15 x-3$ 
B)  $-10 x^{2}+9 x+9$ 
C)  $10 x^{2}+9 x-9$ 
D)  $10 x^{2}-10 x-9$ 
A)  $5 x^{2}+15 x-3$ 
B)  $-10 x^{2}+9 x+9$ 
C)  $10 x^{2}+9 x-9$ 
D)  $10 x^{2}-10 x-9$

Question 15

Find the product
-$\left(-5 m^{3}\right)\left(2 m^{4}\right)$

Accepted Answer

A)  $10 \mathrm{~m}^{6}$ 
B)  $10 \mathrm{~m}$ 
C)  $-10 m^{7}$ 
D)  $-10 \mathrm{~m}$ 
A)  $10 \mathrm{~m}^{6}$ 
B)  $10 \mathrm{~m}$ 
C)  $-10 m^{7}$ 
D)  $-10 \mathrm{~m}$

Question 16

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{-20 x^{10}-40 x^{7}}{-5 x^{4}}$

Accepted Answer

A)  $4 x^{6}-40 x^{7}$ 
B)  $4 x^{6}+8 x^{3}$ 
C)  $-20 x^{10}+8 x^{3}$ 
D)  $12 x^{13}$ 
A)  $4 x^{6}-40 x^{7}$ 
B)  $4 x^{6}+8 x^{3}$ 
C)  $-20 x^{10}+8 x^{3}$ 
D)  $12 x^{13}$

Question 17

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
-$\left(\frac{11 t^{-2}}{t^{5}}\right)^{-3} \cdot \frac{3}{t^{-1}}$

Accepted Answer

A)  $\frac{3 t^{2}}{11^{3}}$ 
B)  $\frac{3 t^{21}}{11^{3}}$ 
C)  $\frac{3 t^{22}}{11^{3}}$ 
D)  $3 \cdot 11 \mathrm{t}^{22}$ 
A)  $\frac{3 t^{2}}{11^{3}}$ 
B)  $\frac{3 t^{21}}{11^{3}}$ 
C)  $\frac{3 t^{22}}{11^{3}}$ 
D)  $3 \cdot 11 \mathrm{t}^{22}$

Question 18

Perform the following division. Explain the rules used for each step.
$$\frac{-30 m^{8} r^{8}}{36 m^{10} r^{2}}$$

Accepted Answer

Reduce the coefficients by div

Question 19

Give the domain and range of the function.
-$f(x)=4 x^{2}-3$

Accepted Answer

A)  Domain: $(-3, \infty)$; range: $(-\infty, \infty)$ 
B)  Domain: $(-\infty, 4)$; range: $(-\infty, \infty)$ 
C)  Domain: $(-\infty, \infty)$; range: $(-\infty, 3)$ 
D)  Domain: $(-\infty, \infty)$; range: $(-3, \infty)$ 
A)  Domain: $(-3, \infty)$; range: $(-\infty, \infty)$ 
B)  Domain: $(-\infty, 4)$; range: $(-\infty, \infty)$ 
C)  Domain: $(-\infty, \infty)$; range: $(-\infty, 3)$ 
D)  Domain: $(-\infty, \infty)$; range: $(-3, \infty)$

Question 20

Perform the indicated operations.
-$(7 m-2)\left(2 m^{2}+m+9\right)$

Accepted Answer

A)  $9 m^{2}+61 m-18$ 
B)  $14 m^{3}+3 m^{2}+61 m-18$ 
C)  $14 \mathrm{~m}^{3}-11 \mathrm{~m}^{2}+61 \mathrm{~m}-18$ 
D)  $14 \mathrm{~m}^{3}+61 \mathrm{~m}-18$ 
A)  $9 m^{2}+61 m-18$ 
B)  $14 m^{3}+3 m^{2}+61 m-18$ 
C)  $14 \mathrm{~m}^{3}-11 \mathrm{~m}^{2}+61 \mathrm{~m}-18$ 
D)  $14 \mathrm{~m}^{3}+61 \mathrm{~m}-18$

Add or subtract as indicated. - $\left(-6 x^{6}+8 x^{8}+4-8 x^{7}\right)-\left(6+5 x^{7}+5 x^{8}+8 x^{6}\right)$

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(\frac{-3 w^{5}}{x}\right)^{4}$

Express the number in scientific notation -0.000000034603

Find the product - $(-9+x)(4 x-4)$

Find the requested value. -If $f(x)=2 x+2$ and $g(x)=8 x^{2}-9 x+5$ , find (fg) $(-5)$ .

$(\mathrm{w}-13)^{2}$

Find the product - $(a-11)(a+11)$

Decide whether the expression has been simplified correctly. - $(2 b)^{4}=2^{4} b^{4}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{x^{2}+11 x+18}{x+2}$

Find the product - $\left(-2 x^{2}-10 y\right)\left(-4 x^{2}-12 y+z\right)$

Find the product - $(m+6)(m-6)$

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+3, g(x)=-4 x-7$

Give the domain and range of the function. - $f(x)=x^{3}+5$

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

Find the product - $\left(-5 m^{3}\right)\left(2 m^{4}\right)$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{-20 x^{10}-40 x^{7}}{-5 x^{4}}$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\left(\frac{11 t^{-2}}{t^{5}}\right)^{-3} \cdot \frac{3}{t^{-1}}$

Perform the following division. Explain the rules used for each step. $\frac{-30 m^{8} r^{8}}{36 m^{10} r^{2}}$

Give the domain and range of the function. - $f(x)=4 x^{2}-3$

Perform the indicated operations. - $(7 m-2)\left(2 m^{2}+m+9\right)$

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

Add or subtract as indicated. - (−6x6+8x8+4−8x7)−(6+5x7+5x8+8x6)\left(-6 x^{6}+8 x^{8}+4-8 x^{7}\right)-\left(6+5 x^{7}+5 x^{8}+8 x^{6}\right)(−6x6+8x8+4−8x7)−(6+5x7+5x8+8x6)

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers. - (−3w5x)4\left(\frac{-3 w^{5}}{x}\right)^{4}(x−3w5​)4

Express the number in scientific notation -0.000000034603

Find the product - (−9+x)(4x−4)(-9+x)(4 x-4)(−9+x)(4x−4)

Find the requested value. -If f(x)=2x+2f(x)=2 x+2f(x)=2x+2 and g(x)=8x2−9x+5g(x)=8 x^{2}-9 x+5g(x)=8x2−9x+5 , find (fg) (−5)(-5)(−5) .

(w−13)2(\mathrm{w}-13)^{2}(w−13)2

Find the product - (a−11)(a+11)(a-11)(a+11)(a−11)(a+11)

Decide whether the expression has been simplified correctly. - (2b)4=24b4(2 b)^{4}=2^{4} b^{4}(2b)4=24b4

Choose the one alternative that best completes the statement or answers the question. Divide - x2+11x+18x+2\frac{x^{2}+11 x+18}{x+2}x+2x2+11x+18​

Find the product - (−2x2−10y)(−4x2−12y+z)\left(-2 x^{2}-10 y\right)\left(-4 x^{2}-12 y+z\right)(−2x2−10y)(−4x2−12y+z)

Find the product - (m+6)(m−6)(m+6)(m-6)(m+6)(m−6)

For the pair of functions, find the product (fg)(x)(f g)(x)(fg)(x) . - f(x)=5x+3,g(x)=−4x−7f(x)=5 x+3, g(x)=-4 x-7f(x)=5x+3,g(x)=−4x−7

Give the domain and range of the function. - f(x)=x3+5f(x)=x^{3}+5f(x)=x3+5

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

Find the product - (−5m3)(2m4)\left(-5 m^{3}\right)\left(2 m^{4}\right)(−5m3)(2m4)

Choose the one alternative that best completes the statement or answers the question. Divide - −20x10−40x7−5x4\frac{-20 x^{10}-40 x^{7}}{-5 x^{4}}−5x4−20x10−40x7​

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - (11t−2t5)−3⋅3t−1\left(\frac{11 t^{-2}}{t^{5}}\right)^{-3} \cdot \frac{3}{t^{-1}}(t511t−2​)−3⋅t−13​

Perform the following division. Explain the rules used for each step. −30m8r836m10r2\frac{-30 m^{8} r^{8}}{36 m^{10} r^{2}}36m10r2−30m8r8​

Give the domain and range of the function. - f(x)=4x2−3f(x)=4 x^{2}-3f(x)=4x2−3

Perform the indicated operations. - (7m−2)(2m2+m+9)(7 m-2)\left(2 m^{2}+m+9\right)(7m−2)(2m2+m+9)

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

Add or subtract as indicated. - $\left(-6 x^{6}+8 x^{8}+4-8 x^{7}\right)-\left(6+5 x^{7}+5 x^{8}+8 x^{6}\right)$

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(\frac{-3 w^{5}}{x}\right)^{4}$

Find the product - $(-9+x)(4 x-4)$

Find the requested value. -If $f(x)=2 x+2$ and $g(x)=8 x^{2}-9 x+5$ , find (fg) $(-5)$ .

$(\mathrm{w}-13)^{2}$

Find the product - $(a-11)(a+11)$

Decide whether the expression has been simplified correctly. - $(2 b)^{4}=2^{4} b^{4}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{x^{2}+11 x+18}{x+2}$

Find the product - $\left(-2 x^{2}-10 y\right)\left(-4 x^{2}-12 y+z\right)$

Find the product - $(m+6)(m-6)$

For the pair of functions, find the product $(f g)(x)$ . - $f(x)=5 x+3, g(x)=-4 x-7$

Give the domain and range of the function. - $f(x)=x^{3}+5$

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

Find the product - $\left(-5 m^{3}\right)\left(2 m^{4}\right)$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{-20 x^{10}-40 x^{7}}{-5 x^{4}}$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\left(\frac{11 t^{-2}}{t^{5}}\right)^{-3} \cdot \frac{3}{t^{-1}}$

Perform the following division. Explain the rules used for each step. $\frac{-30 m^{8} r^{8}}{36 m^{10} r^{2}}$

Give the domain and range of the function. - $f(x)=4 x^{2}-3$

Perform the indicated operations. - $(7 m-2)\left(2 m^{2}+m+9\right)$