Question

Find the quotient when f(x) = x³ + 3x² + 3x + 5 is divided by g(x) = x + 2. Also, find the remainder.

Answer 1

Here, f(x) = x³ + 3x² + 3x + 5 and g(x) = x + 2.
$$\begin{gathered} x^2+x+1 \\ x+2\overline{)x^3+3x^2+3x+5} \\ {x}^3+2x^2 \\ \underline{--} \\ {x}^2+3x+5 \\ {x}^2+2x \\ \underline{--} \\ x+5 \\ x+2 \\ \underline{--} \\ 3 \end{gathered}$$
Hence, the quotient is x² + x + 1 and the remainder is 3.