Introduction to Factorization

We will discuss here about the introduction to factorization.

The method of expressing a given polynomial as a product of two or more polynomials is called factorization.

The polynomials whose product is the given polynomial are called its factors.

You are already familiar with simple factorizations of the following types.

(i) 3x2 + 6 = 3(x2 + 2)

(ii) x2 – 7x = x(x – 7)

(iii) ab + ac + xb + xc = a(b + c) + x(b + c) = (b + c)(a + x), [Factorization by grouping]

In (i), 3 and x2 + 2 are factors of 3x2 + 6; in (ii), x  and x – 7 are factors; in (iii) b + c and a + x are factors of ab + ac + xb + xc.


Use of a2 – b2 = (a + b)(a – b) in Factorization

Factorization of Expressions of the Form a2 – b2 (different of two squares)

We know, (a + b)(a – b) = a2 – b2. So, a2 – b2 = (a + b)(a – b).


Solved Examples on Introduction to Factorization:

1. Factorize: 25a2 – 81b2.

Solution:

25a2 – 81b2

= (5a)2 – (9b)2

= (5a + 9b)(5a – 9b).


2. 16x2 – y2

Solution:

16x2 – y2

= (4x)2 – y2

= (4x + y)(4x – y)


3. a2x2 – b2y2

Solution:

a2x2 – b2y2

= (ax)2 – (by)2

= (ax + by)(ax – by)


4. 2x2 – 18

Solution:

2x2 – 18

= 2(x2 – 9)

= 2(x2 – 32)

= 2(x + 3)(x – 3)






9th Grade Math

From Introduction to Factorization to HOME PAGE




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.



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.

Share this page: What’s this?

Recent Articles

  1. 3-digit Numbers on an Abacus | Learning Three Digit Numbers | Math

    Oct 08, 24 10:53 AM

    3-Digit Numbers on an Abacus
    We already know about hundreds, tens and ones. Now let us learn how to represent 3-digit numbers on an abacus. We know, an abacus is a tool or a toy for counting. An abacus which has three rods.

    Read More

  2. Names of Three Digit Numbers | Place Value |2- Digit Numbers|Worksheet

    Oct 07, 24 04:07 PM

    How to write the names of three digit numbers? (i) The name of one-digit numbers are according to the names of the digits 1 (one), 2 (two), 3 (three), 4 (four), 5 (five), 6 (six), 7 (seven)

    Read More

  3. Worksheets on Number Names | Printable Math Worksheets for Kids

    Oct 07, 24 03:29 PM

    Traceable math worksheets on number names for kids in words from one to ten will be very helpful so that kids can practice the easy way to read each numbers in words.

    Read More

  4. The Number 100 | One Hundred | The Smallest 3 Digit Number | Math

    Oct 07, 24 03:13 PM

    The Number 100
    The greatest 1-digit number is 9 The greatest 2-digit number is 99 The smallest 1-digit number is 0 The smallest 2-digit number is 10 If we add 1 to the greatest number, we get the smallest number of…

    Read More

  5. Missing Numbers Worksheet | Missing Numerals |Free Worksheets for Kids

    Oct 07, 24 12:01 PM

    Missing numbers
    Math practice on missing numbers worksheet will help the kids to know the numbers serially. Kids find difficult to memorize the numbers from 1 to 100 in the age of primary, we can understand the menta

    Read More