Find a polynomial \(q(x)\) such that (x+1)^3+x^2*q(x) has degree less than 2.
i dont want the answer can i just have a hint?
(x + 1)^3 = x^3 + 3x^2 +3x + 1
For our polynomial to have a degree less than 2, we need to cancel the x^3 and 3x^2 terms
So q (x) will do this if it is something like (-x -3)
x^3 + 3x^2 + 3x + 1 + x^2 ( -x - 3) =
x^3 + 3x^2 + 3x + 1 - x^3 - 3x^2 =
3x + 1 and this is a degree < 2
(note that other answers are possible ....but this answer for q(x) seems the easiest )