# Blog

## What is the factor theorem? ## What are the theorems and how to find the linear factorization?

• What the theorems are and how they can be used to find the linear factorization of a polynomial? The Remainder Theorem states that if a polynomial, f (x), is divided by x - k, the remainder is equal to f (k). The Factor Theorem states that the polynomial x - k is a factor of the polynomial f (x) if and only if f (k) = 0.

## How do you prove the converse of the factor theorem?

• According to factor theorem, if f (x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f (x), if f (a)=0. Also, we can say, if (x-a) is a factor of polynomial f (x), then f (a) = 0. This proves the converse of the theorem. Let us see the proof of this theorem along with examples. What is a Factor Theorem?

## How do you find the factor of a polynomial?

• The polynomial, say f (x) has a factor (x-c) if f (c)= 0, where f (x) is a polynomial of degree n, where n is greater than or equal to 1 for any real number, c. Factor theorem example and solution are given below. Go through once and get a clear understanding of this theorem.  