Question

Using remainder theorem, find the remainder when p(x) = x³ − 3x² + 4x + 50 is divided by (x + 3).

Answer 1

$$\begin{gathered} p\left(x\right)=x^3-3x^2+4x+50 \\ \mathrm{According}\mathrm{to}\mathrm{remainder}\mathrm{theorem},\text{w}\mathrm{hen}p\left(x\right)\mathrm{is}\mathrm{divided}\mathrm{by}\left(x+3\right)\mathrm{the}\mathrm{remainder}\mathrm{is}p\left(-3\right). \\ \mathrm{Now}, \\ p\left(-3\right)={\left(-3\right)}^3-3{\left(-3\right)}^2+4\left(-3\right)+50 \\ =-27-27-12+50 \\ =-16 \\ \mathrm{Therefore},\mathrm{remainder}=-16 \end{gathered}$$