Question

If the polynomial x^4 +2x^3+8x^2+12x+18 is divided by the polynomial x^2+5, the remainder comes out to be px+q, find p and q

Answer 1

Using synthetic divison we find that, (x4+2x3+8x2+12x+18) = (x2+5)(x2+2x+3) + 2x + 3 where 2x + 3 is the remainder, Hence p = 2 and q = 3.