Question

Find the value of a for which (x + 1) is a factor of (ax³ + x² – 2x + 4a – 9).

Answer 1

Let f(x) = ax³ + x² – 2x + 4a – 9

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

Using factor theorem, we have

f(−1) = 0
$$\begin{gathered} \Rightarrow a\times {\left(-1\right)}^3+{\left(-1\right)}^2-2\times \left(-1\right)+4a-9=0 \\ \Rightarrow -a+1+2+4a-9=0 \\ \Rightarrow 3a-6=0 \\ \Rightarrow 3a=6 \\ \Rightarrow a=2 \end{gathered}$$
Thus, the value of a is 2.