need help for math exam prep questions.

Question

Find a polynomial  such that  has degree less than .

Answer 1

not going to happen....

it's not a polynomial...

it will be a RATIONAL function....

(x+1)^3 + x^2 *q(x) = Ax+B

(x+1)^2 - (Ax+B) = -x^2 * q(x)

x^3 + 3x^2 + 3x+ 1 - ax - b = -x^2 * q(x)

x^3 + 3x^2 + (3-a)x + (1-b) = -x^2 q(x)

multiplies both sides by -x^2:

- [ x^3 + 3x^2 + (3-a)x + (1-b)]/x^2 = q(x)