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3 years ago

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

Mathematics

1 answer:

galina1969 [7]3 years ago

3 0

<h2>Answer:</h2><h2>g = 2 and h = -5</h2>

Step-by-step 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

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