Finding the divisor

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March 22nd 2011, 04:18 PM
Devi09

Finding the divisor

If you were given the dividend which is a polynomial, the quotient, and remainder what would you have to do to find the divisor?
March 22nd 2011, 04:31 PM
TheEmptySet

Quote:

Originally Posted by Devi09

If you were given the dividend which is a polynomial, the quotient, and remainder what would you have to do to find the divisor?

Let
$p(x)$ be the dividend
$q(x)$ be the quotient
$r(x)$ be the remainder
$m(x)$ be the divisor

$\displaystyle \frac{p(x)}{m(x)}=q(x)+r(x) \iff \frac{m(x)}{p(x)}=\frac{1}{q(x)+r(x)} \iff m(x)=\frac{p(x)}{q(x)+r(x)}$

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