Answer:
The factored form is: [tex]5k^2(h^2 - 3hk - 40k^2)[/tex]
Step-by-step 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
[tex]5k^2(\frac{5h^2k^2}{5k^2} - \frac{15hk^3}{5k^2} - \frac{200k^4}{5k^2}) = 5k^2(h^2 - 3hk - 40k^2)[/tex]
The factored form is: [tex]5k^2(h^2 - 3hk - 40k^2)[/tex]
