Question

How do you divide `(-3x^3 + 6x^2 + 45x)` by `(x -5))`?

Answer 1

The expression resulting is `-3x(x+3)`

Explanation:

The expression can be rewritten as
`-(3x(x^2-2x-15))/(x-5)`
We can also factor the polynomial of the second degree, finding its roots:
`x^2-2x-15=0`
`Delta=4+60=64=8^2`
`x=(2+-8)/2` => `x_1=5; x_2=-3`

So
`-(3x(x^2-2x-15))/(x-5)=-(3xcancel((x-5))(x+3))/cancel((x-5))=-3x(x+3)`