Say we divide by a polynomial of degree 1 (such as "x−3") the remainder will have degree 0 (in other words a constant, like "4"). We will use that idea in the "Remainder Theorem". When we …

In algebra, the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) [1] is an application of Euclidean division of polynomials.

This paper contains a collection of 31 theorems, lemmas, and corollaries that help explain some fundamental properties of polynomials. The statements of all these theorems can be …

The remainder theorem is used to find the remainder without using the long division when a polynomial is divided by a linear polynomial. It says when a polynomial p (x) is divided by (x - …

The Remainder Theorem tells us that, in order to evaluate a polynomial p(x) at some number x = a, we can instead divide by the linear expression x − a. The remainder, r(a), gives the value of …

Use the rational zeros theorem to find rational zeros of a polynomial. Use the Factor Theorem to solve a polynomial equation. In the last section, we learned how to divide polynomials. We can …

The Remainder Theorem states that if a polynomial function 𝑓 (𝑥) f (x) is divided by 𝑥 − 𝑐 x c, then the remainder is 𝑓 (𝑐) f (c). This means we can always compare the remainder by finding 𝑓 (𝑐) f (c) …

Jan 22, 2022 · In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem …

Dec 22, 2025 · We can now use polynomial division to evaluate polynomials using the Remainder Theorem. If the polynomial is divided by x – k, the remainder may be found quickly by …

In algebra, the Polynomial Remainder Theorem states that the remainder upon dividing any polynomial by a linear polynomial , both with complex coefficients, is equal to .