Proof that a-b divides f(a) - f(b).

Question

Given a polynomial function f(x), prove that f(a) - f(b) is divisible by a - b. I tried it with a few examples and it is coming out to be true. Is it true and if so how do we prove it ? Thanks

Does this answer your question? Show that $a - b \mid f(a) - f(b)$ — Crostul, Mar 10 '20 at 18:18
@WuDaozi Do you know how to calculate polynomial division? Try $\frac{a^2-b^2}{a-b}$, $\frac{a^3-b^3}{a-b}$, $\frac{a^4-b^4}{a-b}$, and see what pattern emerges. — Arthur, Mar 10 '20 at 18:33

score 1 · Answer 1 · answered Mar 10 '20 at 18:16

1

Hint: Show first that it is true for monomials. Then for the general case, order terms by degree.

answered Mar 10 '20 at 18:16

Arthur

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Proof that a-b divides f(a) - f(b).

1 Answers1