Factoring Polynomials Formula and Factoring Polynomials Worksheet with Answers

**What is Factorisation?**

Representation of an algebraic expression ( polynomials )as the product of two or more expressions is called factorisation. Each such expression is called a factor of the given algebraic expression. These factors may be numbers, algebraic variables or algebraic expressions.

When the factors of the polynomial are multiplied together, you will get the original polynomial.

## Methods of Factoring Polynomials

There are a certain number of methods by which we can factorise polynomials. Let us discuss these methods.

**(i) Method of common factors**

The first method for factoring polynomials will be factoring out the greatest common factor. It means look at all the terms and determine if there is a factor that is in common to all the terms. If there is, we will factor it out of the polynomial. For example ,Suppose we have to factorise

, 9 = 3 x 3 . Hence

Now the distributive law states that a(b+c) = ab + bc . By using this law

Therefore, we can write

Note that we can always check our factoring by multiplying the terms back out to make sure we get the original polynomial.

Let’s take a look at some more examples.

**Example 1: Factorise .**

**Solution : **

Thus the common factors are and

Therefore

Answer: Thus the factors of are

**Example 2 : Factorise **

**.**

**Solution: **

Thus the common factors are 3 , 3 and i.e. 9y.

Therefore

Answer: The factors of are

**Example 3: Factorise **

**.**

Solution:

Thus the common factors are 3, a, b and c i.e. 3abc.

Therefore

Answer: Thus the factors of are

**Example 4: Factorise **

Solution :

Thus the common factors are and

Therefore

Answer : Factors of are

**(ii)Factoring By Grouping**

Let us try to understand grouping for factorizing with the help of the following examples.

**Example 1: ** **Factorize the polynomial using the method of regrouping of factoring a polynomial.**

**Solution: **For factoring polynomials we observe that we have no common factor among all the terms in the expression

Answer: Therefore the factors of

**Example 2: Factorise **

Solution: There is no common factor among all the terms. Notice that first two terms have a common factor

terms have common factor 1.

So,

=

The factors of

**Example 3 : Factorise **

Solution: There is no common factors in all the terms of

=

Hence, the required factors are

**Example 4: Factorise**

Solution: Grouping the terms, we have

Hence, the required factors = and

**Example 5: Factorise . **

Solution:

=

=

Thus the required factors are

** (iii) Factorisation using Algebraic Identities (****Factoring Polynomials Formulas)**

There are some nice special forms of some polynomials that can make factoring easier for us. Some of them are given below.

**Example 1: Factorise .**

Sol. The polynomial

Now using the identity

.

**Example 2: Factorise **

**.**

**Solution: **can be written as

Now using the identity

=

**Example 3: Factorise .**

Solution:

The expression is of the form where

Now using the identity

=

Now, cannot be factorised further, but (

Again using the same identity , it follows that

.

Answer : Therefore the factors of

**Example 4: Factorise **

**.**

Solution:

=

= [Applying Identity

Answer : Thus the factors of are

**Example 5: Factorise **

**.**

Solution: .

The expression is of the form

Now applying the identity , we get

Answer : Therefore the factors of are

**Example 6: Factorise**

Solution : . Now using the identity

we get .

Answer : Factors of

### Factoring polynomial worksheet PDF

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