What is the factors for x^2-x-20?

Mar 24, 2018

$\left(x - 5\right) \left(x + 4\right)$

Explanation:

What factors of $- 20$ add up to the value of b which is $- 1$?:
$4 , - 5$

$- 4 , 5$

$10 , - 2$

$- 10 , 2$

$20 , - 1$

$- 20 , 1$

It would be $4 , - 5$, therefore:
$\left(x - 5\right) \left(x + 4\right)$, since a is equal to 1

Mar 24, 2018

${x}^{2} - x - 20 = \left(x + 4\right) \left(x - 5\right)$

Explanation:

${x}^{2} - x - 20$

In order to factor, we have to find factors of $- 20$ that when summed together give us $- 1$ (since $- 1$ is the coefficient of the middle term).

Factors of $- 20$:
$\left(- 1 , 20\right) , \left(1 , - 20\right) , \left(2 , - 10\right) , \left(- 2 , 10\right) , \left(- 4 , 5\right) , \textcolor{b l u e}{\left(\left(4 , - 5\right)\right)}$

We see that $\left(4 , - 5\right)$ has two factors for $- 20$ that when summed together equals $- 1$.

So we can write our factor form:

${x}^{2} - x - 20 = \left(x + \textcolor{b l u e}{4}\right) \left(x \textcolor{b l u e}{- 5}\right)$