# How the division algorithm can be used to check the result of the polynomial division.

How the division algorithm can be used to check the result of the polynomial division.
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According to the division algorithm, f(x) and d(x) are the polynomials, where $d\left(x\right)\ne 0$ and the degree of d(x) is less than or equal to the degree of f(x). Then, there exist unique polynomials q(x) and r(x) such that $f\left(x\right)=d\left(x\right)-q\left(x\right)+r\left(x\right)$, where the degree of r(x) is zero or of a lesser degree than d(x).
Consider, polynomial f(x) is the dividend, d(x) is the divisor, q(x) is the quotient and r(x) is the remainder.
In the polynomial division, the dividend is divided by the divisor that gives a quotient and a remainder.
Therefore,
$\frac{f\left(x\right)}{d\left(x\right)}=\frac{1\left(x\right)+r\left(x\right)}{d\left(x\right)}$
$f\left(x\right)=d\left(x\right)\ast q\left(x\right)+r\left(x\right)$