Polynomial remainder theorem

In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials. It states that the remainder of the division of a polynomial ${\displaystyle f(x)}$ by a linear polynomial ${\displaystyle x-a}$ is equal to ${\displaystyle f(a).}$ In particular, ${\displaystyle x-a}$ is a divisor of ${\displaystyle f(x)}$ if and only if ${\displaystyle f(a)=0.}$

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