The factor theorem states that if f (x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f (x) if f (a) = 0. Factor theorem is mainly used to factor the …

The Factor Theorem says that if x=a is a solution to [polynomial]=0, then x−a is a factor of [polynomial]. You use the Theorem with synthetic division.

What if we calculate f (c) and it is 0? ... that means the remainder is 0, and ... ... (x−c) must be a factor of the polynomial! We see this when dividing whole numbers. For example 60 ÷ 20 = 3 with no remainder.

In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if is a (univariate) polynomial, then is a factor of if and only if (that is, is a root of the polynomial).

Jul 23, 2025 · According to the factor theorem, for any polynomial f (x) of degree n ≥ 1 a linear polynomial (x - a) is the factor of the polynomial if f (a) is zero. Let's learn about the factor theorem, …

The Factor Theorem states a direct relationship between the factors and zeros of a polynomial. It says that (x - a) is a factor of the polynomial f (x) if and only if f (a) = 0.

If (x ± h) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then (x ± h) is a factor. Often, factorising a polynomial requires some trial...

Dec 1, 2025 · The factor theorem states that if f (x) is a polynomial of a degree n>0 and a∈R such that f (a) = 0, then (x-a) is a factor of the polynomial f (x). Conversely, if (x-a) is a factor, then a is a zero of …

In this tutorial, we'll look at the factor theorem — what it states and how one can use it. But before we dive into that, let’s get the basics out of the way.

In algebra, the Factor theorem is a theorem regarding the relationships between the factors of a polynomial and its roots. One of it's most important applications is if you are given that a polynomial …