Question

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

Answer 1

`10x^3 +15x^2 + 20x = 5x(2x^2+3x+4)`

Explanation:

We want to factorise `10x^3 +15x^2 + 20x`

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

`10x^3 +15x^2 + 20x = 5x(2x^2+3x+4)`

We then check the discriminant of the quadratic factor, which is
`Delta = b^2-4ac = 9-4(2)(4) < 0`
so we know the quadratic has no real roots, hence it has no real factors (By the factor theorem)

Hence, `10x^3 +15x^2 + 20x = 5x(2x^2+3x+4)`