Question

Question 20
If x + 2a is a factor of $x^5–4a^2{x}^3+2x+2a+3$, then find the value of a.

Answer 1

Let $p\left(x\right)=x^5–4a^2{x}^3+2x+2a+3$
Since x + 2a is a factor of p(x), p (-2a) = 0 [Using Remainder Theorem].
$\therefore (-2a{)}^5–4a^2(-2a{)}^3+2(-2a)+2a+3=0$
$\Rightarrow -32a^5+32a^5–4a+2a+3=0$
$\Rightarrow -2a+3=0$
$\Rightarrow 2a–3=0$
$\therefore a=\frac{3}{2}$
Hence, the value of a is $\frac{3}{2}$.