With this problem, you should first look at the equation for the area of a trapezoid. That is A = (1/2)(B1 + B2)*H. We know what A, B1, and B2 are so you just need to solve for height. So, based on the equation:
\(3x^{3} -16 x^{2} + 31x-20 = (1/2)(x+5+ x^{2} -5x)*h\)
Next, you would have:
\(6x^{3} -32x^{2} +62x-40=(x^{2}-4x+5)*h\)
Next solve for h by dividing the polynomials like so:
\(h = (6 x^{3}-32 x^{2} +62x-40)/( x^{2} -4x+5)\)
Using long division you get:
\(h = 6x-8\)
