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