How can the polynomial 6d4 + 9d³ – 12d² be factored?

Answer 1

The given polynomial 6d^4 + 9d^3 - 12d^2 can be factored by finding the Greatest Common Factor (GCF) of the terms. The GCF in this case is 3d^2.

So, we can rewrite the polynomial as:
6d^4 + 9d^3 - 12d^2 = 3d^2(2d^2 + 3d - 4)

Now, the quadratic trinomial 2d^2 + 3d - 4 can be factored further.

Using the quadratic formula or factoring techniques, we can find that 2d^2 + 3d - 4 = (2d - 1)(d + 4)

Therefore, the fully factored form of the given polynomial is:
6d^4 + 9d^3 - 12d^2 = 3d^2(2d - 1)(d + 4)