Question

Find the value of 'a' if (x $-$ 2) is a factor of 2x³ $-$ 6x² + 5x + a.

Answer 1

$$\begin{gathered} \mathrm{Let}p\left(x\right)=2x^3-6x^2+5x+a \\ \mathrm{When}x-2=0,\mathrm{we}\mathrm{have}x=2 \\ \mathrm{Putting}x=2\mathrm{in}p\left(x\right),\mathrm{we}\mathrm{get}: \\ p\left(2\right)=2{\left(2\right)}^3-6{\left(2\right)}^2+5\left(2\right)+a \\ =16-24+10+a \\ =a+2 \\ \left(x-2\right)\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}p\left(x\right). \\ \mathrm{By}\mathrm{factor}\mathrm{theorem},\mathrm{we}\mathrm{have}: \\ p\left(2\right)=0 \\ \Rightarrow a+2=0 \\ \therefore a=-2 \end{gathered}$$