Question

Show that (x + 2) is a factor of f(x) = x³ + 4x² + x − 6.

Answer 1

$$\begin{gathered} \mathrm{Given}:f\left(x\right)=x^3+4x^2+x-6 \\ \mathrm{Now},f\left(-2\right)={\left(-2\right)}^3+4{\left(-2\right)}^2+\left(-2\right)-6 \\ =-8+16-2-6 \\ =0 \\ \therefore \left(x+2\right)\mathrm{is}\mathrm{a}\mathrm{}\mathrm{factor}\mathrm{}\mathrm{of}f\left(x\right)=x^3+4x^2+x-6. \end{gathered}$$