# Is it possible to factor y= 2x^2 + x - 1 ? If so, what are the factors?

Dec 6, 2015

$y = \left(x + 1\right) \left(2 x - 1\right)$

#### Explanation:

$y = 2 {x}^{2} + x - 1$ is a quadratic equation with the form $a {x}^{2} + b x + c$, where $a = 2 , b = 1 , c = - 1$

Use the AC method to factor this equation.

Multiply $a$ times $c$.

$2 \times - 1 = - 2$

Determine two numbers that when added equal $1$, and when multiplied equal $- 2$. The numbers $2$ and $- 1$ meet the criteria.

Rewrite the expression with $2 x$ and $- x$ in place of $x$.

$2 {x}^{2} + 2 x - x - 1$

Group the first two terms and the second two terms.

$\left(2 {x}^{2} + 2 x\right) - \left(x + 1\right)$

Factor out the GCF $2 x$ from the first pair of terms.

$2 x \left(x + 1\right) - \left(x + 1\right)$

Factor out $\left(x + 1\right)$.

$\left(x + 1\right) \left(2 x - 1\right)$

$y = \left(x + 1\right) \left(2 x - 1\right)$