How Does the Remainder Theorem Simplify Polynomial Division?

[Jordan1994]

Q2.) Show all working out.

a) Find the remainder when $$x^3+2x^2-5x-3$$ is divided by $$x-2$$.

b) Find the remainder when $$x^3-3x^2-x+3$$ is divided by $$x-3$$.

 

[HallsofIvy]

Q2.) Show all working out.

a) Find the remainder when $$x^3+2x^2-5x-3$$ is divided by $$x-2$$.

b) Find the remainder when $$x^3-3x^2-x+3$$ is divided by $$x-3$$.

You titled this "remainder theorem question". What does the "remainder theorem" say?