# How do you factor 10x^3 +15x^2 +20x?

Oct 30, 2016

$10 {x}^{3} + 15 {x}^{2} + 20 x = 5 x \left(2 {x}^{2} + 3 x + 4\right)$

#### Explanation:

We want to factorise $10 {x}^{3} + 15 {x}^{2} + 20 x$

We can see immediately that $5 x$ is a common factor, so first lets factor that out:

$10 {x}^{3} + 15 {x}^{2} + 20 x = 5 x \left(2 {x}^{2} + 3 x + 4\right)$

We then check the discriminant of the quadratic factor, which is
$\Delta = {b}^{2} - 4 a c = 9 - 4 \left(2\right) \left(4\right) < 0$
so we know the quadratic has no real roots, hence it has no real factors (By the factor theorem)

Hence, $10 {x}^{3} + 15 {x}^{2} + 20 x = 5 x \left(2 {x}^{2} + 3 x + 4\right)$