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helppls

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Polynomial Division Math Problem Help

Let $f(x)$ and $g(x)$ be polynomials.

Suppose $f(x)=0$ for exactly three values of $x$: namely, $x=-3,4,$ and $8$.

Suppose $g(x)=0$ for exactly five values of $x$: namely, $x=-5,-3,2,4,$ and $8$.

Is it necessarily true that $g(x)$ is divisible by $f(x)$? If so, carefully explain why. If not, give an example where $g(x)$ is not divisible by $f(x)$.

Part 2:

Generalize: for arbitrary polynomials $f(x)$ and $g(x)$, what do we need to know about the zeroes (including complex zeroes) of $f(x)$ and $g(x)$ to infer that $g(x)$ is divisible by $f(x)$?

(If your answer to Part 1 was "yes", then stating the generalization should be straightforward. If your answer to Part 1 was "no", then try to salvage the idea by imposing extra conditions as needed. Either way, prove your generalization.)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Polynomial Division Math Problem Help

hi helppls

if

then

so f doesn't divide g. 

That should be enough for you to answer this question.

Bob

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