Question

For which the value of m, x + 3 is the factor of the polynomial x³ $-$ 2mx + 21?

Answer 1

Let $p\left(x\right)=x^3-2mx+21$.

(x + 3) is the factor of the polynomial $p\left(x\right)=x^3-2mx+21$.

$$\begin{gathered} \therefore p\left(-3\right)=0 \\ \Rightarrow {\left(-3\right)}^3-2m\times \left(-3\right)+21=0 \\ \Rightarrow -27+6m+21=0 \\ \Rightarrow 6m-6=0 \\ \Rightarrow 6m=6 \\ \Rightarrow m=1 \end{gathered}$$
Thus, the value of m is 1.