Question 1

Simplify the expression $$\left( \frac{x$$^{-2}$$}{x^3$} \$$right)^4$$ and write your answer using positive exponents only.

Accepted Answer

Question 2

Simplify the expression $$\frac{16m^2$n^3p^0$}{24m^3$n^2p^2$}$$ and write your answer using positive exponents only.

Accepted Answer

$$\frac{2n}{3mp^2$}$$

Question 3

Given the polynomial $$P(x) = 3x^4$ - 4x^3$ + 2x^2$ - 12x - 6$$, what is the degree of $$P(x)$$?

Accepted Answer

$$4$$

Question 4

What is the leading coefficient of the polynomial $$P(x) = 3x^4$ - 4x^3$ + 2x^2$ - 12x - 6$$?

Accepted Answer

$$3$$

Question 5

Divide $$x^4$$ + $$3x^3$$ + $$5x^2 - 4$ by x + 3$ using polynomial long division. What is the remainder?

Accepted Answer

$$-31$$

Question 6

Factor completely: $$36m^2n^3$ - 6mn^2$ + 12mn$.

Accepted Answer

$$6mn(6n^2 - n + 2$$)$$

Question 7

Solve for $$t$$: $$3(4t - 3) = 0.$$

Accepted Answer

$$t = 1$$

Question 8

Solve for $$p$$: $$p^2 + 4 = 32$.

Accepted Answer

$$p = \pm 4$$

Question 9

Given the rational function $$f(x) = \frac{x^2$ - 4}{x^2$ - 4}$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

$$(-\infty, -2) \cup (-2, 2) \cup (2, \infty)$$

Question 10

A rectangular garden has an area of $$280$$ square feet. The width is $$4$$ feet longer than one-half the length. What is the length of the garden?

Accepted Answer

$$20$$ feet

Question 11

Factor completely: $$x^3 - 27$.

Accepted Answer

$$(x - 3)(x^2$ + 3x + 9)$$

Question 12

Simplify: $$\left( \frac{xy^2$}{z^3$} \$$right)^4$$.

Accepted Answer

$$\frac{x^4$y^8$$}{$$z^{12}$$}$

Question 13

Subtract and simplify: $$\frac{2x^2$ - 11}{x - 1} - \frac{11}{x - 1}.$$

Accepted Answer

$$\frac{2x^2$ - 22}{x - 1}$$

Question 14

Solve for $$a$$: $$a^2 - 6a - 7 = 10$.

Accepted Answer

$$a = 10, a = -1$$

Question 15

Factor completely: $$x^3 - 81$.

Accepted Answer

$$(x - 9)(x^2$ + 9x + 81)$$

Question 16

Divide and simplify: $$\frac{x^2$ - 7x + 8}{x^2$ - 6x + 8} \div \frac{x^2$ - 4x + 4}{x^2$ - 12x + 32}.$$

Accepted Answer

$$\frac{(x - 1)}{(x - 4)}$$

Question 17

Add and simplify: $$\frac{8}{y^2$ + 3y} + \frac{15}{y + 3}.$$

Accepted Answer

$$\frac{8 + 15y}{y(y + 3)}$$

Question 18

A chemical solution is made by mixing two solutions: one with $$x$$ grams of salt per liter and another with $$2x$$ grams per liter. If the final mixture is $$10$$ liters and contains $$15$$ grams of salt per liter, what is the value of $$x$$?

Accepted Answer

Question 19

Solve for $$k$$: $$k^5$$ + $$2k^2 = k + 5$.

Accepted Answer

No real solution

Intermediate Algebra Practice Test Guidance

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