# How do you factor x^2 + x - 42?

Sep 21, 2015

$\left(x + 7\right) \left(x - 6\right)$

#### Explanation:

Factoring quadratic equations is usually a trial and error thing (at least for me). Here's how I answered it in my head.

First, I thought of the factors of ${x}^{2}$. The only possible ones are $x$ and $x$.

Next, I thought: What two factors of -42 are equal to $1$ (since that is the coefficient of $x$) when added?
The two numbers that I thought of were -6 and 7, since $- 6 + 7 = 1$.

Therefore, my factors are $\left(x + 7\right)$ and $\left(x - 6\right)$.

You can try double-checking this by multiplying $\left(x + 7\right)$ and $\left(x - 6\right)$.

If you don't like "guessing" the factors, you can also use the quadratic formula for that. Though I suggest you don't since it is time consuming.
x=(-b±sqrt(b^2-4ac))/(2a)

Sep 21, 2015

$\left(x - 6\right)$$\left(x + 7\right)$

#### Explanation:

Cross factorise it! It's a little hard to explain so you should watch a video which would help you understand even better.

To check:
Expand the brackets! You will get the same answer.