Is the quotient of two polynomials always a polynomial? Answersmaxima: how
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Let $f(x)$ be a polynomial with coefficients.If $r$ is an integral root of $f$, then prove that the polynomial $fracf(x)x-r$ also has coefficients.
The first degree is a factor of $f(x)$ if $r$ is an integral root.The quotient is a function of the divident and the divisor, and we can say that the remainder is $0.It's a result of the fact that if the divident $Delta(x)$ is used, it becomes an integer polynomial.The quotient $q(x)$ and the rest of the quotient ($r)(x)(3) are both floating coefficients.This can be seen from the long-division scheme.In such a situation, the leading coefficients of the quotient and the divident will be the same.
P.S.If the divisor is not monic, the quotient and the rest are in general rational polynomials.The division of polynomials is generally defined.Can it take place inside the divisor if it is monic?