Question

Synthetic Division:

4) (2x^6 - x^5 + 3x^2 + 2x - 4) / (x+2)

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} & x^6& x^5 & x^4 & x^3 & x^2 & x^1 & x^0 \\ -2& 2& -1 & 0 & 0 & 3 & 2 & -4 \\ & & -4 & 10 & -20 & 40 & -86 & 168 \\ \hline & 2 & -5 & 10 & -20 & 43 & -84 & 164 \\ \end{array}$$

Therefore

$$\dfrac{2x^6-x^5+3x^2+2x-4}{x+2}$$

$$=2x^5-5x^4+10x^3-20x^2+43x-84+\dfrac{164}{x+2}$$