Answer:

if x-a is a factor of this polynomial x⁵-a²x³+2x+a+1 then

when we substitute x=a in the equation we must get zero as answer

so moving on

let the polynomial be p(x)=x⁵-a²x³+2x+a+1

p(a)=0

then

a⁵-a²(a³)+2a+a+1=0

a⁵-a⁵ +3a+1=0

0+3a+1=0

from here

a=-1/3!!