Determine the coeffiecients in front x and x^3 (x^2+9x+3)(x^3-4x+7/x)

See the answer under your first question.

coefficient in front of x³ = 3 - 4 = -1.

coefficient in front of x = 7 - 12 = -5.

How did I get that?

First, ask, how many ways you get the form of ax³ if you pick 2 terms and multiply?

First way,3 times x³

Second way, -4x times x²

No other ways.

So the coefficient of x³ = 3 + (-4) = 3 - 4 = -1

You do the coefficient of x one as above too.