Subscribe to our YouTube channel for the latest videos, updates, and tips.
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
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.
May 19, 25 02:53 PM
May 18, 25 04:33 PM
May 17, 25 04:04 PM
May 17, 25 03:47 PM
May 16, 25 11:13 AM
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.