Question

what is the factorization of the trinomial below?
3x^3-18x^2+24x

A. 3x(x-2)(x-4)
B. 3(x-2)(x+4)
C. 3(x^2-2)(x+4)
D. 3x(x-2)(x+4)

Answer 1

3x^3 - 18x^2 + 24x

We can factor a 3x from each term.

3x(x^2 - 6x + 8)

Now, we can factor the trinomial even further.

Split the middle term.

3x(x^2 - 2x - 4x + 8)

3x(x(x - 2) - 4(x - 2)

3x(x - 4)(x - 2) is the fully factored form of the trinomial.

The correct answer is A.