Module
In
Math
(Factor Theorem)
Submitted By:
Jean Anne Marie C. Romulo
G10- Aguinaldo
Submitted To:
Sir Nick Hermoso
Factor Theorem
- Objectives
- Determine the formula of Factor Theorem
- Able to explain what Factor Theorem is and use this to solve a problem.
- Topic
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial [pic 1] has a factor [pic 2] if and only if [pic 3] (i.e. [pic 4] is a root).
The point of the Factor Theorem is the reverse of the Remainder Theorem: If you synthetic-divide a polynomial by x = a and get a zero remainder, then, not only is x = a a zero of the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor of the polynomial (courtesy of the Factor Theorem).
It is commonly applied to factorizing and finding the roots of polynomial equations. The theorem states that [pic 5] is a factor of a polynomial f(x)if [pic 6];that is, r is a root off(x). Factor theorem problems are typically solved by applying synthetic division and then checking for a zero remainder. The remainder theorem is often used with the factor theorem. It states that if a polynomial f(x) is divided by a linear divisor [pic 7], the remainder is f(r). If [pic 8], then the remainder is 0 and [pic 9], showing that [pic 10] is a factor of f(x).