# How do you factor the trinomial  x^2 - 7x + 12?

Apr 6, 2018

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

Here's how I did it:

#### Explanation:

Two factor a trinomial in form $a {x}^{2} + b x + c$, you must find two numbers that:
$\textcolor{red}{a} {x}^{2} + \textcolor{m a \ge n t a}{b} {x}^{2} + \textcolor{b l u e}{c}$

• Multiply up to $\textcolor{red}{a} \textcolor{b l u e}{c}$
• Add up to $\textcolor{m a \ge n t a}{b}$

In this question, that means the two numbers must:

• Multiply up to $\left(\textcolor{red}{1}\right) \left(\textcolor{b l u e}{12}\right) = 12$
• Add up to $\textcolor{m a \ge n t a}{- 7}$

These two numbers are $- 3$ and $- 4$:
$- 3 \cdot - 4 = 12$
$- 3 - 4 = - 7$

So now we put them into factored form:
$\left(x - 3\right) \left(x - 4\right)$

Hope this helps!

Apr 6, 2018

The factors always multiply to C (12) and add to Bx (7x).
In this case, the answer is (x-4)(x-3) because multiplying two negatives equal a positive and adding two negatives are still negative.