Factors of a Polynomial
We will discuss here about the basic concept of factors of a polynomial.
We have, f(x) = ϕ(x) ∙ ψ(x) + R(x), where R(x) is the remainder and ψ(x) is the quotient when f(x) is divided by ϕ(x).
If R(x) = 0, f(x) is divided by ϕ(x) and f(x) = ϕ(x) ∙ ψ(x).
ϕ(x) and ψ(x) are factors of f(x).
Examples on factors of a polynomial:
(i) If x2 - x - 12 is divided by x - 4 then
Therefore, the remainder = 0, and x^2 - x - 12 = (x - 4)(x + 3).
Therefore, (x - 4) and (x + 3) are factors of the quadratic polynomial x^2 - x - 12.
(ii) If x^3 + 2x^2 + x + 2 is divided by x + 2 then
Therefore, the remainder = 0, and x^3 + 2x^2 + x + 2 = (x + 2)(x^2 + 1).
Therefore, (x + 2) and (x^2 + 1) are factors of the cubic polynomial x^3 + 2x^2 + x + 2.
● Factorization
- Polynomial
- Polynomial Equation and its Roots
- Division Algorithm
- Remainder Theorem
- Problems on Remainder Theorem
- Factors of a Polynomial
- Worksheet on Remainder Theorem
- Factor Theorem
- Application of Factor Theorem
From Factors of a Polynomial to HOME
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Worksheet on 8 Times Table | Printable Multiplication Table | Video
Mar 18, 25 03:30 PM
Worksheet on 8 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home. -
Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals
Mar 18, 25 02:47 PM
Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V… -
Conversion of Roman Numeration | Roman Numerals |Hindu Arabic Numerals
Mar 18, 25 02:12 PM
We will learn the conversion of Roman numeration. First we will learn how to convert numbers in roman numerals. 1. Convert 579 in roman numerals. -
Rules of Roman Numeration |Roman Number System|Roman Numeration System
Mar 18, 25 09:41 AM
We will learn about Roman Numeration and its rules. We know that there are seven basic Roman Numerals. They are I, V, X, L, C, D and M. These numerals stand for the number 1, 5, 10, 50, 100, 500 -
Divisible by 2 | Test of Divisibility by 2 |Rules of Divisibility by 2
Mar 17, 25 04:04 PM
A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.