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Units 5-6 Review

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Last updated almost 4 years ago
17 questions
Note from the author:
Formula Sheet
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Question 1
1.

Match the equivalent expressions.

Draggable itemarrow_right_altCorresponding Item
a^{2} - b^{2}
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(a+bi)(a-bi)
a^{3}+b^{3}
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(a-b)(a+b)
a^{2} + b^{2}
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(a+b)(a^{2}-ab+b^{2})
a^{3}-b^{3}
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(a-b)(a^{2}+ab+b^{2})
Question 2
2.

What are the zeroes of the following polynomial?

9x^{3} + 9x^{2} - 4x - 4

Enter your answer in "x={#, #...} format, with exactly one space after each comma. List the real zeroes first in increasing order, then the nonreal with the negative first. Use fractions rather than decimals.

Question 3
3.

What are the zeroes of the following polynomial?

4x^{2} - 81

Enter your answer in "x={#, #...} format, with exactly one space after each comma. List the real zeroes first in increasing order, then the nonreal with the negative first. Use fractions rather than decimals.

Question 4
4.

What are the zeroes of the following polynomial?

x^{3} - 64

Enter your answer in "x={#, #...} format, with exactly one space after each comma. List the real zeroes first in increasing order, then the nonreal with the negative first. Use fractions rather than decimals.

Question 5
5.

Let f(x) = x^{3} - 5x^{2} + 5x - 12.

What is the remainder of \frac{f(x)}{(x - 4)}?

Enter your answer as a number, no spaces.

Question 6
6.

Let f(x) = 2x^{3} +5x^{2} + 5x +12.

What is the remainder of \frac{f(x)}{(x+2)}?

Enter your answer as a number, no spaces.

Question 7
7.

Let f(x) = x^{3} - 10x +4.

What is the remainder of \frac{f(x)}{(x+3)}?

Enter your answer as a number, no spaces.

Question 8
8.

Match the term with the description of its end behaviors.

Draggable itemarrow_right_altCorresponding Item
odd-degree polynomial with positive leading coefficient
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x\rightarrow\infty, f(x)\rightarrow -\infty; x\rightarrow -\infty, f(x)\rightarrow -\infty
even-degree polynomial with negative leading coefficient
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x\rightarrow\infty, f(x)\rightarrow\infty; x\rightarrow -\infty, f(x)\rightarrow\infty
odd-degree polynomial with negative leading coefficient
arrow_right_alt
x\rightarrow\infty, f(x)\rightarrow -\infty; x\rightarrow -\infty, f(x)\rightarrow \infty
even-degree polynomial with positive leading coefficient
arrow_right_alt
x\rightarrow\infty, f(x)\rightarrow\infty; x\rightarrow -\infty, f(x)\rightarrow -\infty
Question 9
9.

Simplify the expression.

2\sqrt[3]{2x} + \sqrt[3]{54x}

Enter your answer in simplest radical form.

Question 10
10.

Simplify the expression.

(1+ \sqrt{10})(2-\sqrt{10})

Enter your answer in simplest radical form, no spaces.

Question 11
11.

Simplify the expression.

(5x)^{5/3} \cdot \sqrt[3]{x}

Enter your answer in simplest radical form.

Question 12
12.

Simplify the expression.

\sqrt{2x} \cdot \sqrt{8x^{6}}

Enter your answer in simplest radical form.

Question 13
13.

Solve for x.

\sqrt[3]{x-7} = -1

Enter your answer as a number, no spaces.

Question 14
14.

Solve for x.

2\sqrt{x+5} =16

Enter your answer as a number, no spaces.

Question 15
15.

Solve for x.

20-\sqrt{2x+6} =16

Enter your answer as a number, no spaces.

Question 16
16.

What is the inverse of the function f(x) = \sqrt{2x-6}?

Use "y=..." format, no spaces.

Question 17
17.

What is the inverse of the function f(x) = \sqrt[3]{x+6}-1? Do NOT distribute.

Use "y=..." format, no spaces.