# How do you factor 2y^2+7y+5?

Jul 12, 2018

$\left(2 y + 5\right) \left(y + 1\right)$

$2 {y}^{2}$ only has $y$ and $2 y$ as factors

Similarly 5 only has factors 1 and 5

Jul 12, 2018

2y^2+7y+5=color(blue)((2y+5)+(y+1)

#### Explanation:

Factor:

$2 {y}^{2} + 7 y + 5$

Use the $\text{ac}$ method to factor this trinomial. $a = 2$ and $c = 5$

Multiply $2$ by $5$ to get $10$. Find two numbers that when added equal $7$ and when multiplied equal $10$. The numbers $5$ and $2$ meet the requirements.

Split the middle term $7 y$ to $5 y + 2 y$. This method is also sometimes called "splitting the middle term."

$2 {y}^{2} + 5 y + 2 y + 5$

Factor out common terms in the first two and second two terms.

$y \left(2 y + 5\right) + \left(2 y + 5\right)$ $\leftarrow$ understood to be $1 \left(2 y + 5\right)$

Factor out the common term $\left(2 y + 5\right)$.

$\left(2 y + 5\right) + \left(y + 1\right)$