Answer:
g = 2 and h = -5
Step-by-step explanation:
To find the product with unknown values of variables, multiply the terms and equate the value to the given product.
[tex](7d^{2} - 3d + g)(3d^{2} + hd - 8)[/tex] = [tex]21d^{4} + 7hd^{3} - 56d^{2} - 9d^{3} - 3hd^{2} + 24d + 3gd^{2} + ghd - 8g[/tex]
[tex](7d^{2} - 3d + g)(3d^{2} + hd - 8)[/tex] = [tex]21d^{4} + (7h-9) d^{3} + (3g-56-3h)d^{2} + (24+gh)d -8g[/tex] ... (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
