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
- How to Understanding Onto (Surjective) Functions
- 8th Grade OSTP Math Worksheets: FREE & Printable
- How to Prepare for the AFOQT Math Test?
- FREE 4th Grade PSSA Math Practice Test
- Top 10 Free Websites for SAT Math Preparation
- How to Make Math into a Fun Experience
- Full-Length PSAT 10 Math Practice Test
- Top 10 Free Websites for GED Math Preparation
- 5th Grade ACT Aspire Math Practice Test Questions
- 5th Grade TCAP 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.