# Is it possible to factor y=x^3+5x^2-14x ? If so, what are the factors?

Dec 15, 2015

Yes; $x = - 7 , 0 , 2$

#### Explanation:

Original Equation:
$y = {x}^{3} + 5 {x}^{2} - 14 x$

Factor out an $x$:
$y = x \left({x}^{2} + 5 x - 14\right)$

Factor inside the parentheses (factors of $A C$ that add up to $B$):
––Factors of $- 14$ that add up to $5$

You should get $7$ and $- 2$

Now plug it back into the equation:
$y = x \left(x - 2\right) \left(x + 7\right)$

$x$
$\left(x - 2\right)$
$\left(x + 7\right)$
To find $x$, set each factor equal to $0$ and solve.
$x = 0$
$x = 2$
$x = - 7$