Question

If x + 1 is a factor of the polynomial 2x³ + ax² + 4x + 1, then a = _________.

Answer 1

Let f(x) = 2x³ + ax² + 4x + 1

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

$$\begin{gathered} 2{\left(-1\right)}^3+a{\left(-1\right)}^2+4\left(-1\right)+1=0 \\ \Rightarrow 2\left(-1\right)+a\left(+1\right)+4\left(-1\right)+1=0 \\ \Rightarrow -2+a-4+1=0 \\ \Rightarrow a-5=0 \\ \Rightarrow a=5 \end{gathered}$$

Hence, a = 5.