Question

show that (x-2),(x+3)and (x-7) are the factors of x^₃-6x^₂-13x+42

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^3-6{\mathrm{x}}^2-13\mathrm{x}+42 \\ \mathrm{Now}\mathrm{if}\mathrm{x}-2\mathrm{is}\mathrm{factor}\mathrm{so}\mathrm{x}=2\mathrm{will}\mathrm{satisfy} \\ \mathrm{f}\left(2\right)=2^3-6\times 2^2-13\times 2+42 \\ =0 \\ \mathrm{So}\mathrm{it}\mathrm{is}\mathrm{a}\mathrm{factor}. \\ \mathrm{f}\left(-3\right)={\left(-3\right)}^3-6\times {\left(-3\right)}^2-13\times -3+42 \\ =0 \\ \mathrm{So}\mathrm{it}\mathrm{is}\mathrm{a}\mathrm{factor}. \\ \mathrm{Similarly},\mathrm{f}\left(7\right)=0\mathrm{so}\mathrm{it}\mathrm{is}\mathrm{also}\mathrm{a}\mathrm{factor}. \\ \mathrm{Regards} \end{gathered}$$