Question

If x + 1 is a factor of the polynomial ax³ + x² – 2x + 4a – 9, then a = __________.

Answer 1

Let f(x) = ax³ + x² – 2x + 4a – 9

It is given that one factor of f(x) is (x + 1).

Therefore, $f\left(x\right)=0\mathrm{when}x=-1$.

On putting x = –1 in f(x) = 0, we get

$$\begin{gathered} a{\left(-1\right)}^3+{\left(-1\right)}^2-2\left(-1\right)+4a-9=0 \\ \Rightarrow -a+1+2+4a-9=0 \\ \Rightarrow 3a-6=0 \\ \Rightarrow 3a=6 \\ \Rightarrow a=2 \end{gathered}$$

Hence, if x + 1 is a factor of the polynomial ax³ + x² – 2x + 4a – 9, then a = 2.