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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?

 Mar 20, 2020
 #1
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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

 Mar 20, 2020
 #2
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Thanks!! This really helped!

qwertyzz  Mar 20, 2020

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