monomial factors?

Question

Given that (2x+1) is a factor of m(x)=6x^7 + 15x^6 - 9x^5 - 9x^4,
1.....Factor out any monomial factors

2.....now, factor out (2x+1) as well

3.....now, completely factor m(x)

Answer 1

Monomial factor is 3x^4 The factorization is

3x^4 * (2x^3 + 5x^2 - 3x - 3)

I cannot see how 2x+1 is a factor of 2x^3 + 5x^2 - 3x - 3; polynomial division does not result in integral coefficient and also leaves a remainder.