Units 5-6 Review
star
star
star
star
star
Last updated almost 4 years ago
17 questions
Note from the author:
Formula Sheet
Formula Sheet
1
Match the equivalent expressions.
Match the equivalent expressions.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
a^{2} + b^{2} | arrow_right_alt | (a+bi)(a-bi) |
a^{2} - b^{2} | arrow_right_alt | (a-b)(a+b) |
a^{3}+b^{3} | arrow_right_alt | (a+b)(a^{2}-ab+b^{2}) |
a^{3}-b^{3} | arrow_right_alt | (a-b)(a^{2}+ab+b^{2}) |
1
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.
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.
1
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.
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.
1
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.
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.
1
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.
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.
1
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.
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.
1
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.
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.
1
Match the term with the description of its end behaviors.
Match the term with the description of its end behaviors.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
odd-degree polynomial with positive leading coefficient | arrow_right_alt | x\rightarrow\infty, f(x)\rightarrow -\infty; x\rightarrow -\infty, f(x)\rightarrow -\infty |
even-degree polynomial with negative leading coefficient | arrow_right_alt | 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 |
1
Simplify the expression.
2\sqrt[3]{2x} + \sqrt[3]{54x}
Enter your answer in simplest radical form.
Simplify the expression.
2\sqrt[3]{2x} + \sqrt[3]{54x}
Enter your answer in simplest radical form.
1
Simplify the expression.
(1+ \sqrt{10})(2-\sqrt{10})
Enter your answer in simplest radical form, no spaces.
Simplify the expression.
(1+ \sqrt{10})(2-\sqrt{10})
Enter your answer in simplest radical form, no spaces.
1
Simplify the expression.
(5x)^{5/3} \cdot \sqrt[3]{x}
Enter your answer in simplest radical form.
Simplify the expression.
(5x)^{5/3} \cdot \sqrt[3]{x}
Enter your answer in simplest radical form.
1
Simplify the expression.
\sqrt{2x} \cdot \sqrt{8x^{6}}
Enter your answer in simplest radical form.
Simplify the expression.
\sqrt{2x} \cdot \sqrt{8x^{6}}
Enter your answer in simplest radical form.
1
Solve for x.
\sqrt[3]{x-7} = -1
Enter your answer as a number, no spaces.
Solve for x.
\sqrt[3]{x-7} = -1
Enter your answer as a number, no spaces.
1
Solve for x.
2\sqrt{x+5} =16
Enter your answer as a number, no spaces.
Solve for x.
2\sqrt{x+5} =16
Enter your answer as a number, no spaces.
1
Solve for x.
20-\sqrt{2x+6} =16
Enter your answer as a number, no spaces.
Solve for x.
20-\sqrt{2x+6} =16
Enter your answer as a number, no spaces.
1
What is the inverse of the function f(x) = \sqrt{2x-6}?
Use "y=..." format, no spaces.
What is the inverse of the function f(x) = \sqrt{2x-6}?
Use "y=..." format, no spaces.
1
What is the inverse of the function f(x) = \sqrt[3]{x+6}-1? Do NOT distribute.
Use "y=..." format, no spaces.
What is the inverse of the function f(x) = \sqrt[3]{x+6}-1? Do NOT distribute.
Use "y=..." format, no spaces.