MHB How Does the Remainder Theorem Simplify Polynomial Division?

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The Remainder Theorem states that the remainder of a polynomial f(x) when divided by x - c is equal to f(c). For the polynomial x^3 + 2x^2 - 5x - 3, substituting c = 2 yields a remainder of -1. For the polynomial x^3 - 3x^2 - x + 3, substituting c = 3 results in a remainder of 0. This theorem simplifies polynomial division by allowing direct evaluation rather than performing long division. Understanding this theorem is essential for efficiently finding remainders in polynomial expressions.
Jordan1994
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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 $$x-3$$.
 
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Jordan1994 said:
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?
 

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