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:

$Q(x)=\frac{R(x)}{P(x)}$

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

$Q(x)=\frac{2x^3+2x^2-3x-3}{x+1}$

We can rewrite this expression by factorizing:

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

and this is our answer.

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