Question

If ( x $-2$ ) is a factor of $x^3-m{x}^2+10x-20$ then find the value of m.

Answer 1

Let $p\left(x\right)=x^3-m{x}^2+10x-20$.

It is given that (x − 2) is a factor of $p\left(x\right)=x^3-m{x}^2+10x-20$.

$$\begin{gathered} \therefore p\left(2\right)=0 \\ \Rightarrow {\left(2\right)}^3-m\times {\left(2\right)}^2+10\times \left(2\right)-20=0 \\ \Rightarrow 8-4m+20-20=0 \\ \Rightarrow 8-4m=0 \\ \Rightarrow 4m=8 \\ \Rightarrow m=2 \end{gathered}$$
Thus, the value of m is 2.