# How do you factor the expression 2x^2 - 11x + 12?

Jan 28, 2016

$\left(2 x - 3\right) \left(x - 4\right)$

#### Explanation:

Looking at the ${x}^{2}$ coefficient, $2$, we know that the coefficients of $x$ in each factor can only be $1$ and $2$ since no other integers multiply to 2.

Therefore we can set up the factors as:
$\left(2 x - \text{＿＿")*(x - "＿＿}\right)$

We know that both of the operations in the factors must be subtraction because $12$ is positive and $- 11$ is negative.

To find out what goes in the blanks, we need to check the factors of 12:

$1$ and $12$
$2$ and $6$
$3$ and $4$

$1$ and $12$ can't work, because no matter what side each is on, $12$ times anything will be greater than $11$.

$2 \cdot 2 + 1 \cdot 6$ is $10$, and $2 \cdot 6 + 1 \cdot 2$ is $14$, neither of which are 11.

Finally, we can try pair $3$ and $4$. Feel free to try both of them yourself to see why the first must be $3$ and the second must be $4$, not the other way around!