College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Are you Ready for College Algebra? - B. Diagnostic Test: Algebraic Expressions - Page XVIII: 2


(a) 2$\mathcal{x}$(2$\mathcal{x}$ + 1) (b) 3$\mathcal{x}$$\mathcal{y}$($\mathcal{y}$ - 2$\mathcal{x}$) (c) ($\mathcal{x}$ + 3)($\mathcal{x}$ + 5) (d) ($\mathcal{x}$ - 2)($\mathcal{x}$ + 1) (e) (2$\mathcal{x}$ - 3)($\mathcal{x}$ +4) (f) ($\mathcal{x}$ + 4)($\mathcal{x}$ - 4)

Work Step by Step

These equations are solved by different types of factoring. The first type of factoring is seen in (a) and (b). The second is seen in c-f. In (a) the problem is: 4$\mathcal{x^2}$ + 2$\mathcal{x}$. To simplify factor 2$\mathcal{x}$ out of the equation. This leaves 2$\mathcal{x}$(2$\mathcal{x}$ + 1). Question (b) is solved using the same method. In (c) the problem is: ($\mathcal{x^2}$ + 8$\mathcal{x}$ +15). When factoring look for numbers that could been multiplied to equal the number with no variable, and added/subtracted to equal the integer with one variable. In this case it is 3 and 5. This leaves ($\mathcal{x}$ + 3)($\mathcal{x}$ + 5). Questions (c), (d), (e), and (f) are solved the same way, with slight differences. In (e) 2$\mathcal{x}$ must be in the same parenthesis with 3 to get the beginning equation. In (f) the integers with $\mathcal{x}$ will cancel out. If you are unsure if you put the integers in the correct places, solve the equation. I feel you get the original it was correct.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.