# 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

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

1. ### Method of H.C.F. |Highest Common Factor|Factorization &Division Method

Apr 13, 24 05:12 PM

We will discuss here about the method of h.c.f. (highest common factor). The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers. Let us…

2. ### Factors | Understand the Factors of the Product | Concept of Factors

Apr 13, 24 03:29 PM

Factors of a number are discussed here so that students can understand the factors of the product. What are factors? (i) If a dividend, when divided by a divisor, is divided completely

3. ### Methods of Prime Factorization | Division Method | Factor Tree Method

Apr 13, 24 01:27 PM

In prime factorization, we factorise the numbers into prime numbers, called prime factors. There are two methods of prime factorization: 1. Division Method 2. Factor Tree Method

4. ### Divisibility Rules | Divisibility Test|Divisibility Rules From 2 to 18

Apr 13, 24 12:41 PM

To find out factors of larger numbers quickly, we perform divisibility test. There are certain rules to check divisibility of numbers. Divisibility tests of a given number by any of the number 2, 3, 4…