How can the polynomial 6d^4 + 9d^3 - 12d^2 be factored?
A. 3d^2(2d^2+3d-4)
B. 3d^2(3d^2 + 6d - 9)
C. 3d(d^3 + 3d^2 - 4)
D. 6d^2(d^2 + 3d^3 - 6)
The correct answer is A. 3d^2(2d^2+3d-4)
To factor the polynomial 6d^4 + 9d^3 - 12d^2, we can first look for the greatest common factor (GCF) of all the terms, which is 3d^2. Factoring out the GCF gives us:
3d^2(2d^2 + 3d - 4)
So the polynomial can be factored as 3d^2 multiplied by the quadratic expression 2d^2 + 3d - 4.