Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Prerequisite Skills Diagnostic Test: 15


$(3x + 5)(x - 2)$

Work Step by Step

Factor $3x^{2}-x-10$ First set up the x's in the binomial. $(cx +or- n)(cx +or- n)$ To have $3x^{2}$ in the original equation the two $x$'s in the binomial multiply together. Thus the $x$'s have coefficients. 3 is a prime number so its only factors are 3 and 1. Therefore in one of the parentheses the $x$ has a coefficient of 3 and the other has a coefficient of 1 $(3x +or- n)(1x +or- n)$ Now we need to find n in the expression above both n values must multiply to -10 and add (when the expression is expanded) -1x. Also we must take into account the 3 coefficient. To start list out the factors of -10: -1,10 1,-10 -2,5 2,5 Think which of these factor pairs when one number is multiplied by three and subtracted by the other leaves us with -1 Immediately we can discount the 1,10 pairs because there would be too large of a difference, leaving us to choose between the -2,5 and the 2,-5 factor pairs. $2*3=6$ and $5-6=1$ so we know that the $2$ will not be in the same parentheses as the $3x$ $(3x +or- 5)(1x +or- 2)$ Last we need to figure out the signs within the parentheses. As mentioned before $5-6=1$ so we want 6 to be negative, thus we write $-2$ $(3x +or- 5)(1x - 2)$ And because we want 5 to be positive we write $+5$ $(3x + 5)(x - 2)$ To check expand the expression and will match the original equation
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.