lwfrgin

2021-02-11

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

broliY

Skilled2021-02-12Added 97 answers

According to the division algorithm, f(x) and d(x) are the polynomials, where $d(x)\ne 0$ 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 $f(x)=d(x)-q(x)+r(x)$ , 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,

$\frac{f(x)}{d(x)}=\frac{1(x)+r(x)}{d(x)}$

$f(x)=d(x)\ast q(x)+r(x)$

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,

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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