# How do you factor 2n^2 - 7n + 3?

May 18, 2016

$\left(2 x - 1\right) \left(x - 3\right)$

#### Explanation:

The general equation that factors as $\left(a x + b\right) \left(c x + d\right)$ multiplies out to be $a c {x}^{2} + \left(a d + b c\right) x + b d$. This shows that the coefficient of the middle term is made up from factors of the coefficients of the outer terms.

Thus is this case we need factors of $2$ and $\left(- 3\right)$ that will add (or subtract) to give $- 7$.

The only possible factors are $2$ and $1$, and $3$ and $1$.

The result is therefore $\left(2 x - 1\right) \left(x - 3\right)$