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?
Start by looking at the constant terms of both equations, which are g and -16. We know that when we multiply the two polynomials together, the constant terms of the new equaion is only affected by the constant terms of the previous equations. In other words, g * (-8) = -16. This means that g = 2. Next, to find the value of h, we can look at the coefficient of "d" in the product. we know that the coefficient of d in the product comes from multiplying a linear "d" with a constant. That means that (-3d) * (-8) + hd * g = 14d. This expands to:
24d + hd*g = 14d, and subtracting on both sides, we get:
hd * g = -10 d
Remember that we already found that g = 2, giving us
hd * 2 = -10 d
hd = -5d
h = -5.
Since the problem asks for g + h, we get :
2 - 5 = -3