If the product of a linear binomial and (x ^ 2-2x-1) does not contain a linear term, find the linear binomial, and let the linear binomial be x + a

If the product of a linear binomial and (x ^ 2-2x-1) does not contain a linear term, find the linear binomial, and let the linear binomial be x + a

(x+a)(x²-2x-1)
=x³-2x²-x+ax²-2ax-a
=x³-(2-a)x²-(1+2a)x-a
∵ does not contain a single term
∴1+2a=0
a=-1/2