Question 1

Simplify the expression $$ (2x^3$)(3x^{-1})^2$ $$ and write your answer in the form $$ ax^b . $$What is the value of $$ a $$ and $$ b $$?

Accepted Answer

$$ 18x $$

Question 2

A shoe company is combining the inventory from two stores. Store A has $$ \frac{1}{2}q^2$ + \frac{7}{2} $$, and Store B has $$ 3q^2$ - \frac{4}{5}q + \frac{1}{4} . $$What is the combined inventory as a single polynomial?

Accepted Answer

$$ \frac{7}{2}q^2$ - \frac{4}{5}q + \frac{15}{4} $$

Question 3

Which expression is equivalent to $$ 210d^2$ - 63d $$?

Accepted Answer

$$ 21d(10d - 3) $$

Question 4

Simplify the expression $$ (4x^2$y^3)(2xy^2$) $$ and write your answer in the form $$ ax^by^c .$$

Accepted Answer

$$ 8x^3$y^5$$ $

Question 5

Factor the expression $$ 12x^2$ - 8x . $$Which of the following is correct?

Accepted Answer

$$ 4x(3x - 2) $$

Question 6

Which of the following is equivalent to $$ (x^2$ - 9) $$?

Accepted Answer

$$ (x - 3)(x + 3) $$

Question 7

A chemist mixes two solutions. The first has $$ 2x^2$ + 5x $$ grams of a chemical, and the second has $$ 3x^2$ - 2x + 4 $$ grams. What is the total amount of chemical in the mixture?

Accepted Answer

$$ 5x^2$ + 3x + 4 $$

Question 8

Which of the following is the result of multiplying $$ (x + 2)(x - 5) $$?

Accepted Answer

$$ x^2$ - 3x - 10 $$

Question 9

Simplify $$ (2x^2$y^3)^2$ .$$

Accepted Answer

$$ 4x^4$y^6$$ $

Question 10

Which of the following is the greatest common factor (GCF) of $$ 18x^3$y $$ and $$ 24x^2$y^2$$ $?

Accepted Answer

$$ 6x^2$y $$

College Algebra Review: Simplifying, Combining, and Factoring Expressions

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