Question

Let p(x)=9x^3-3x^2-5x-2=(x-1)(3x+2)Q(x)+ax+b.
i) Show that a+b=-1
ii) Show that (-2/3a) +b=-8/3
iii) Hence, find the remainder when O(x) is divided by 3x^2-x-2.

Thank you!

Answer 1

(9x^3-3x^2-5x-2)/((x-1)(3x+2)) = 3x + (-x+2)/((x-1)(3x+2))
So Q(x) = 3x
ax+b = -x+2 so clearly a+b = 1
in fact, a = -1 and b=2, so (-2/3)(-1)+2 = 8/3
no idea what O(x) is, but I think you have enough information by now