Question

The product of $7d^2-3d+g$ and $3d^2+hd-8$ is $21d^4-44d^3-35d^2+14d-16$. What is $g+h$?

Answer 1

g = 2 and h = -5

Explanation:

To find the product with unknown values of variables, multiply the terms and equate the value to the given product.

`(7d^(2) - 3d + g)(3d^(2) + hd - 8)` =
`21d^(4) + 7hd^(3) - 56d^(2) - 9d^(3) - 3hd^(2) + 24d + 3gd^(2) + ghd - 8g`

`(7d^(2) - 3d + g)(3d^(2) + hd - 8)` =
`21d^(4) + (7h-9) d^(3) + (3g-56-3h)d^(2) + (24+gh)d -8g` ... (1)

Comparing eq(1) to the product given in question,

-8g = -1

g = 2

24 + gh = 14, sub g =2,

24 + 2h = 14

h = -5