# Factorization of Polynomials  ## Factorization of Polynomials:

When a polynomial or an expression is expressed as a product of two or more polynomials, then each polynomial in the product is a factor of the given polynomial. The process of expressing a polynomial as a product of its factors is called factorization.

### Factorization by taking out Common Factors:

If a factor is common to all the terms of a polynomial, then it is placed outside the brackets. The figures to be placed inside the brackets are obtained by dividing each term of the given polynomial by the common factor.

### Factorization by Grouping the Terms:

The terms in the given expression can be arranged in groups of two or three to get a common factor. The given expression can then be factorized by taking out the common factor.

### Factorization of the difference between two Squares:

When the given expression is written as the difference between two squares, it is factorized using the formula a2 – b2 = (a + b) (a – b).

### Factorization of Trinomial ax2 + bx + c by splitting the middle term:

Let the given trinomial be ax2 + bx + c. The terms of the trinomial should be arranged in a descending or ascending order of the powers of x. In order to factorize ax2 + bx + c, we should find two numbers p and q whose sum equals the coefficient of x i.e. b and the product equals the product of the coefficients of x2, and the constant term i.e. (a) x (c).

We split the middle-term bx as px + qx and then factorize it by grouping.

### Factorization of the sum and the difference of the Two Cubes:

The sum and the difference of the two cubes can be factorized using: