Question

Use remainder theorem to find the value of k, it being given that when x³ + 2x² + kx + 3 is divided by (x − 3), then the remainder is 21.

Answer 1

$$\begin{gathered} \mathrm{Let}p\left(x\right)=x^3+2x^2+kx+3 \\ \mathrm{Now},p\left(3\right)={\left(3\right)}^3+2{\left(3\right)}^2+3k+3 \\ =27+18+3k+3 \\ =48+3k \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{}\mathrm{that}\mathrm{}\mathrm{the}\mathrm{}\mathrm{remainder}\mathrm{}\mathrm{is}21 \\ \therefore 3k+48=21 \\ \Rightarrow 3k=-27 \\ \Rightarrow k=-9 \end{gathered}$$