Find a polynomial q(x) such that (x+1)^3+x^2*q(x) has degree less than 2.
I don't know where to start so can someone give me a place where to solve. I don't need answers because then I can solve it by myself.
(x + 1)^3 = x^3 + 3x^2 + 3x + 1
All we require is that some q(x) can be found such that the x^3 and 3x^2 terms in the first polynomial can be canceled
Let q (x) be (-x - 3)
So notice that
x^2 * q(x) = x^2 (-x - 3) = -x^3 -3x^2
x^3 + 3x^2 + 3x + 1 + (-x^3 - 3x^2) =
3x + 1
And this is a polynomial of less than degree 2
(Note that the choice of q(x) isn't unique.... there are many other possibilities)