Question

factor x^3+1=x^2+x

Answer 1

x^3+1=x^2+x
x^3-x^2-x+1=0
let f(x) =x^3-x^2-x+1
By remainder thm,
f(1) =1^3-1^2-1+1 =0
therefore (x-1) is a factor

therefore f(x) =x^3-x^2-x+1 = (x-1) ( x^2 -1) = (x+1)(x-1)^2
x^3-x^2-x+1=0
(x+1)(x-1)^2 =0
(x+1) =0 or (x-1)^2 =0
x=-1 or x=1