Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Review Exercises - Page 479: 19


$$(5y - 2)(y - 3)$$

Work Step by Step

First, we take the coefficient of the first term and take its factors and put them first in the parentheses: $($5y $)$ $($y $)$ Since the last term is positive and the middle term is negative, this means that the operations within the two parentheses should be two subtraction signs: $($5y$ - ) $(y$ - )$ Now, we check the factors for the last term to see which one would fit. The factors for $6$ are $6$ and $1$ and $3$ and $2$. It seems like $3$ and $2$ would fit: $$(5y - 2)(y - 3)$$ We check by the FOIL method to make sure. According to the FOIL method, we multiply the first terms, then the outer, then the inner, and, finally, the last terms: $$5y^2 - 15y - 2y + 6$$ Combine like terms to simplify: $$5y^2 - 17y + 6$$ We see that this equation is the same one we were factoring, which means that our factoring was correct.
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