Remainder and Factor Theorems
The factor theorem is mainly used for factoring polynomials and finding \(n\) roots of polynomials. In this step-by-step guide, you learn more about the factor and remainder theorems.

When a polynomial is divided by a linear polynomial, the remainder theorem is used to find the remainder.
A step-by-step guide to the remainder and factor theorems
According to the remainder theorem, if we divide a polynomial \(P(x)\) by the factor \((x – a)\); which is essentially not an element of a polynomial; you will find a smaller polynomial with the remainder. This remainder obtained is actually a value of \(P(x)\) at \(x = a\), specifically \(P(a)\). So basically, \((x -a)\) is the divisor of \(P(x)\) if and only if \(P(a) = 0\). It is applied to factorize polynomials of each degree in an elegant manner.
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 \(f(a) = 0\). In other words, we can say that \((x – a)\) is a factor of \(f(x)\) if \(f(a) = 0\).
Difference between the factor theorem and the remainder theorem
The remainder and factor theorems are similar but refer to two different concepts. The remainder theorem relates the remainder of the division of a polynomial by a binomial with the value of a function at a point. The factor theorem relates the factors of a given polynomial to its zeros.
Related to This Article
More math articles
- Top 10 Algebra 2 Textbooks in 2024 (Expert Recommendations)
- Using Decimals and Fractions to Solve One-Step Addition and Subtraction
- How Students Can Understand Math for Free
- FREE 6th Grade Common Core Math Practice Test
- Matching a Model with a Ratio
- FREE 5th Grade STAAR Math Practice Test
- How to Study Math Effectively?
- ASVAB Math Practice Test Questions
- 5 Best GED Math Study Guides
- 7th Grade Scantron Math Worksheets: FREE & Printable
What people say about "Remainder and Factor Theorems - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.