How can the polynomial 6d^4 + 9d^3 - 12d^2 be factored?
To factor the polynomial 6d^4 + 9d^3 - 12d^2, we can first find the common factor among all the terms. In this case, the common factor is 3d^2:
= 3d^2(2d^2 + 3d - 4)
Now, we need to factor the quadratic expression 2d^2 + 3d - 4. We can use the quadratic formula or try factoring by splitting the middle term:
= 3d^2(2d^2 + 4d - d - 4)
= 3d^2(2d(d + 2) - 1(d + 2))
= 3d^2(d + 2)(2d - 1)
Therefore, the polynomial 6d^4 + 9d^3 - 12d^2 can be factored as 3d^2(d + 2)(2d - 1).