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

Accepted Answer

$ 8x^3y^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^2y^3)^2 $.

Accepted Answer

$ 4x^4y^6 $

Question 10

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

Accepted Answer

$ 6x^2y $

College Algebra Review: Simplifying, Combining, and Factoring Expressions

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