In Algebra, Polynomial Factoring is the process of expressing a polynomial equation as a product of two or more similar polynomials. Each polynomial as a product of the given polynomial equation. For example (x - 2) and (x + 2) are the factors of x^{2} - 4
x^{2} - 4 = (x - 2) (x + 2)
Thus factoring is mainly used for solving or simplifying polynomial expressions. The process of polynomial factoring is also called as the resolution into factors.

How to Find Factoring of Polynomial: There are three methods (common factors, grouping terms and using formulas) are used to find polynomial factors in common

Factoring Polynomials by Common Factor: First we have to find the common factor for the given polynomial equation. If a given algebraic polynomial equation A contains common factor B, then divide each term of equation A by common factor B and you will get an expression C. Now B and C are the factors of A and it can be expressed as A = B x C

Example: Find the factors for the polynomial equation 7x^{5}y^{3} + 4 x^{2}y^{3} + 10 xy^{3}?
Solution: In the above equation xy^{3} is common factor.
7x^{5}y^{3} + 4 x^{2}y^{3} + 10 xy^{3} = xy^{3} (7x^{5}y^{3}/xy^{3} + 4 x^{2}y^{3}/xy^{3} + 10 xy^{3}/xy^{3})
7x^{5}y^{3} + 4 x^{2}y^{3} + 10 xy^{3} = xy^{3} (7x^{4}+4x+10)

Factoring Polynomials by Grouping terms If the Polynomial Equation don't have common factors then group the terms. By grouping terms in a appropriate manner you can get a common factor.
Example: Find polynomial factors for the below equation
x^{2} +x - 2xy - 2y
Solution: x^{2} +x - 2xy - 2y = x^{2} - 2xy +x - 2y
Take X as common for first two terms
= x(x - 2y) + (x - 2y)
= (x - 2y) (x + 1)
So the factors for x^{2} +x - 2xy - 2y are (x - 2y) and (x + 1)

Try Yourself Find the polynomial Factors for the below equations
1. ab - 2c - cb + 2a
2. a^{3} - 2a^{2} - 2a + 4
3. a^{3} - a^{2} - ba + b
4. 2x^{3} - x^{2} + 2x - 1
5. 8a^{3} + 4a^{2} + 4a + 2

Examples Problems 1. Find factors of the equation 4a^{2} + 12ab + 9b^{2} Solution: The given polynomial equation can be written as follows
4a^{2} + 12ab + 9b^{2} = (2a)^{2} + 2 (2a)(3b) + (3b)^{2} The above equation can be simplified by using (x + y)^{2} = (2a + 3b)^{2}