# A HORRIBLE Remainder Theorem Problem

Algebra

### A HORRIBLE Remainder Theorem Problem

$$P(x)$$$$\equiv$$ $$P_{n }x^n + P_{n-1 }x^{n-1}+ ...+P_{0 }$$ is divided by $$(x - a)$$, show that the remainder is $$P(a)$$
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### Re: A HORRIBLE Remainder Theorem Problem

You think this is "HORRIBLE"? I've seen much worse!

Any polynomial, P(x), divided by x- a, has a "quotient" and "remainder": $$\frac{P(x)}{x- a}= Q(x)+ \frac{r}{x- a}$$. Since x- a is linear, the quotient, Q, has degree one less than P and r is a constant. From that P(x)= Q(x)(x- a)+ r. Setting x= a, P(a)= Q(a)(0)+ r= r.

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