Question

P(z)-Q(z) = R(z); P(z) = z+1 and R(z) = 2z³ + 2z²-3z-3, what is Q(z)?

Answer 1

Since the R(x) function is given by the following expression

`P(x)\cdot Q(x)=R(x)`

Solving for Q(x), we have:

`Q(x)=(R(x))/(P(x))`

If we substitute the expressions for both functions, we're going to have:

`Q(x)=(2x^3+2x^2-3x-3)/(x+1)`

We can rewrite this expression by factorizing:

`\begin{gathered} Q(x)=(2x^(3)+2x^(2)-3x-3)/(x+1) \\ =(2x^2(x+1)-3(x+1))/(x+1) \\ =((2x^2-3)(x+1))/(x+1) \\ =2x^2-3 \end{gathered}`

and this is our answer.

`Q(x)=2x^2-3`