Question

Factor the trinomial. Factor out the GCF first.
5h^2k^2 – 15hk^3 – 200k^4

Answer 1

The factored form is:
`5k^2(h^2 - 3hk - 40k^2)`

Explanation:

The factorization of the trinomial is given by the multiplication of the greatest common factor of each coefficient(numeric, h and k), put it in front, and divide each term by it.

Numeric:

GCF between 5, 15 and 200.

We keep dividing while all factors can be divided by the same number

5 - 15 - 200|5

1 - 3 - 40

No other possible division, so the numeric GCF is 5.

Coefficient h

To the 2, to the 1, and does not appear(to the 0). So the GCF is 0.

Coefficient k

2, 3 and 4. The GCF is 2.

So

`5k^2((5h^2k^2)/(5k^2) - (15hk^3)/(5k^2) - (200k^4)/(5k^2)) = 5k^2(h^2 - 3hk - 40k^2)`

The factored form is:
`5k^2(h^2 - 3hk - 40k^2)`