Find the remainder when the polynomial x^5 - 4x^3 + 7x^2 - 3 is divided by (x - 1)(x + 2). I think there is a way to do this using Remainder Theorem, but I have no idea how.
We can use long division
I got 4x+9 but I'm not sure
i suggest you search up polynomial division, there are some great tutorials like khan academy that are free
Remainder theorem will get you there.
q(x) will be a cubic and r(x) will be linear, (one degree lower than the quadratic on the bottom line), so let r(x) = ax + b.
Multiply throughout by (x - 1)(x + 2) to get
and now substitute x = 1 and x = -2.
That gets you a pair of simultaneous equations in a and b which you can solve.