Question

Question 22
If x + 1 is a factor of $a{x}^3+x^2–2x+4a–9$, then find the value of a.

Answer 1

Let $p\left(x\right)=a{x}^3+x^2–2x+4a–9$
Since, x + 1 is a factor of p(x), p(-1) = 0 [Using Remainder Theorem].
$\therefore a(-1{)}^3+(-1{)}^2–2(-1)+4a–9=0$
$\Rightarrow -a+1+2+4a-9=0$
$\Rightarrow 3a–6=0\Rightarrow 3a=6$
$\Rightarrow a=\frac{6}{3}=2$
Hence, the value of a is 2.