# Is it possible to factor y=3x^3+30x^2+75x ? If so, what are the factors?

May 30, 2018

$y = 3 x {\left(x + 5\right)}^{2}$

#### Explanation:

$y = 3 {x}^{3} + 30 {x}^{2} + 75 x$

We can see that $3 x$ is a factor.

$\therefore y = 3 x \left({x}^{2} + 10 x + 25\right)$

Which we can write as $3 x \left({x}^{2} + 2 x \times 5 + {5}^{2}\right)$

Now remember: ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

Hence. $\left({x}^{2} + 10 x + 25\right) = {\left(x + 5\right)}^{2}$

$\therefore y = 3 x {\left(x + 5\right)}^{2}$