How do you factor the expression x^3 + 5x^2 - 7x -35?

Dec 13, 2015

$\left(x - \sqrt{7}\right) \left(x + \sqrt{7}\right) \left(x + 5\right) \text{ }$ or

(x^2-7))(x+5)

Explanation:

We can try factor by grouping, since there are four terms.

$\left({x}^{3} + 5 {x}^{2}\right) + \left(- 7 x - 35\right)$

Factor out the greatest common factor of each group

$\textcolor{red}{{x}^{2}} \left(x + 5\right) \textcolor{red}{- 7} \left(x + 5\right)$

What is the common factor of he expression?

$\implies \textcolor{red}{\left({x}^{2} - 7\right)} \left(x + 5\right)$ You may leave the answer like this

Or like this....(because difference of square)
$\implies \left(x - \sqrt{7}\right) \left(x + \sqrt{7}\right) \left(x + 5\right)$