Question

If $(x+2a)$ is a factor of $x^5-4a^2{x}^3+2x+2a+3$, then the value of a is____.

Answer 1

Let p(x) = $x^5-4\left(a{)}^2\right(x{)}^3+2x+2a$
g(x) = x + 2a
g(x) = 0
x + 2a = 0
x = – 2a
Therefore, zero of g(x) = – 2a

p ( – 2a) = $(–2a{)}^5–4(a{)}^2(–2a{)}^3+2(–2a)+2a+3$ = 0
$–32(a{)}^5+32(a{)}^5–2a+3$ = 0
– 2a = – 3
a = 3/2