# Is it possible to factor y=4x^2+19x - 5 ? If so, what are the factors?

Mar 26, 2018

$y = \left(x + 5\right) \left(4 x - 1\right)$

#### Explanation:

Factor:

$y = 4 {x}^{2} + 19 x - 5$

You can factor the right-hand side by using the "splitting the middle term" method.

Multiply the coefficient of the first term by the constant.

$4 \times - 5 = - 20$

Find two numbers that when added equal $- 19$, which is the coefficient of the middle term, and that multiply to $- 20$. The numbers $20$ and $- 1$ meet the requirements.

Split $19 x$ as the sum of $20 x$ and $- x$.

$y = 4 {x}^{2} + 20 x - x - 5$

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

$y = 4 x \left(x + 5\right) - \left(x + 5\right)$

It is understood that $- \left(x + 5\right)$ is $- 1 \left(x + 5\right)$.

Factor out the common term $x + 5$.

$y = \left(x + 5\right) \left(4 x - 1\right)$