Factoring Polynomials

What is factoring a polynomial?

Factoring a polynomial is the process of expressing a higher-degree polynomial as the product of lower-degree polynomials. For example, the polynomial f(x) = 7x² – 21x can be factorized as 7x(x-3), where 7, x, and x-3 are the factors of the given polynomial.

What are the methods for factoring polynomials?

There are a lot of methods for factoring polynomials, including factoring by grouping, factoring using the Sridharacharya Formula, factoring quadratic polynomials using the splitting the middle term method, using algebraic identities to factorize different polynomials, etc.

What is the difference between a factor and a root of a polynomial?

Factor is the lower-degree polynomial that can evenly divide the given polynomial and leave no remainder.

On the other hand, the root, or zero, of a polynomial is the real number for which the value of the polynomial becomes zero.

For example, for the polynomial f(x) = x²+ 2x+1 = (x + 1)², (x + 1) is the factor of the polynomial, and x = -1 is the root of the polynomial.

How can you check if a factor is correct?

If the factors of the given polynomial are correct, then the product of all the factors is the polynomial itself. In other words, by multiplying all the factors of a polynomial together, we end up with the polynomial itself.

How to Factorize Polynomials in 3 Degree?

Follow the following steps to factorize a three-degree polynomial.

• Step 1: For polynomial f(x) find its factor x – a such that f(a) = 0 by the hit and trial method.
• Step 2: Using the long division method divide f(x) by x – a to get a two-degree polynomial.
• Step 3: Factorize the two-degree polynomial obtained by the methods as discussed in the article.

Now, the three-degree polynomial f(x) is factorized.

Factoring Polynomials: A basic algebraic concept called factoring polynomials involves breaking down a polynomial equation into simpler parts. Factoring can be used to solve equations, simplify complicated expressions, and locate the roots or zeros of polynomial functions. 

In several fields of mathematics, including engineering, physics, and computer science, the ability to factor is a crucial skill. Finding the common factors, or roots, of the equation and breaking them down into a set of simpler expressions are the general steps involved in factoring a polynomial. 

In this article, we have provided details about factoring polynomials, steps to factorize polynomials, with solved examples and practice problems on it.