How to Use Factor Theorem?
Factor Theorem is used widely in solving the polynomial equation.
We can learn about the use of factor theorem by going through the example discussed below,
Example: Find the factor of x2 – 4x + 3.
Solution:
Given polynomial,
f(x) = x2 – 4x + 3
by hit and try method,
taking x = 1
f(1) = 12 -4(1) + 3 = 0
Thus, x -1 is the factor of x2 – 4x + 3
again taking x = 3
f(3) = 32 – 4(3) + 3 = 0
Thus, x -3 is the factor of x2 – 4x + 3
Factor Theorem
Factor theorem is used for finding the roots of the given polynomial. This theorem is very helpful in finding the factors of the polynomial equation without actually solving them.
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, its proof, and others in detail in this article.
Table of Content
- What is the Factor Theorem?
- Factor Theorem Statement
- Factor Theorem Formula
- Zero of a Polynomial
- Factor Theorem Proof
- How to Use Factor Theorem?
- Using the Factor Theorem To Factor a Cubic Polynomial
- Factor Theorem and Remainder Theorem
- Factor Theorem Examples