## Introductory Algebra for College Students (7th Edition)

$$(3x + 2)(x + 5)$$
First, we take the coefficient of the first term and take its factors and put them first in the parentheses: $($3x $)$ $($x $)$ Since the last term is positive, this means that the operations within the two parentheses should be two plus signs: $($3x$+ )$(x$+ )$ Now, we check the factors for the last term to see which one would fit. The factors for $10$ are $10$ and $1$ and $5$ and $2$. It seems like $5$ and $2$ would fit: $$(3x + 2)(x + 5)$$ 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: $$3x^2 + 2x + 15x + 10$$ Combine like terms to simplify: $$3x^2 + 17x + 10$$ We see that this equation is the same one we were factoring, which means that our factoring was correct.