# How do you factor: y= x^3 + x^2 − 20x ?

Dec 2, 2015

Factor $y = {x}^{3} + {x}^{2} - 20 x$

#### Explanation:

$y = x Y = x \left({x}^{2} + x - 20\right)$. Factor $Y$

Find 2 numbers knowing sum (1) and product (-20).
Factor pairs of $- 20 \to \left(- 2 , 10\right) \left(- 4 , 5\right)$. This sum is $- 4 + 5 = 1 = b$.

Therefore, the 2 numbers are $- 4$ and $5$.

Factored form:

$y = x Y = x \left(x - 4\right) \left(x + 5\right)$