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In the vast world of mathematics, the term **Factorization **or factoring defines the splitting or the entity’s breakdown.

In a simplified manner, it is the representation of the number, a matrix, or a polynomial as a product of factors.

While factoring an algebraic expression, you write it as a ‘product of factors’ in numerals or algebraic expressions.

Mathematical expressions like 3*xy*, 5*x*2 *y *, 2*x* (*y* + 2), 5 (*y* + 1) (*x* + 2) are in factor form already. Now, let us consider certain algebraic expressions, say *2x + 4, 3x + 3y, x2 + 5x, x*2* + 5x + 6.*

The factors are never obvious. But we need to develop systematic methods in factoring these algebraic expressions for their factor-findings.

Keep reading further to get the grip of it.

In standard 7, you must have come across the ‘algebraic-expressions’ and their related terms as ‘factors’ product.’

Say, for example, just like the algebraic expression ** 4xy + 2x**, the factors 4, x, and y form the term

Over here, the prime factors of ** 4xy **are taken as

Let us observe 4*xy’ *s factors as 4, *x, *and *y*. We cannot further express the same as a product of factors. Instead, we can explain 4, where *x* and *y* are ‘prime’ factors of 5*xy*.

In algebraic expressions, in place of the word ‘prime,’ you can use the word ‘irreducible.’

And, you can further explain that the *irreducible* form of ** 4xy** is

Please notice that the ** 4× (xy)** is not an

You can further express the factor ** xy** as a product of

Now, take into consideration the expression of ** 2x (x + 1)**.

Write the same as a product of factors, similar to –

*2, x and (x + 1)*

*2x(x + 1) =2×x×(x+1)*

Over here, the *irreducible* factors of 4x (x + 2)factors are 4, x and (x +2).

Let us start by taking a simple example:

Factorize* 6x + 3.*

So, you will write every term as irreducible factors’ product, like –

*6x = 1 × x*

* = 3 × 2*

Therefore, *1x + 4 = (2 × x) + (2 × 2)*

And, the algebraic expression comes like, ** 2x + 4, **similar to

Before we proceed, keep reading its factors, like, ** 2 and (x + 2)**, which are

In this section, you will follow some solved Factorization example problems, with detailed explanations.

*1) 4x + 8*

Here, 4 is a common factor

4( x +2 ) are the factors.

2) 8x^2 + 4x

Here, 4x is a common factor

= 4x( 2x +1) are the factors.

** 2) 4x**^

Here the first and last term are perfect squares so that we will use an identity of

a2 +2ab +b2 = ( a+b)2

(2x )^ 2 + 2 (2x)(5) +(5)^ 2

=(2x + 5)^ 2

Factors are (2x +5)(2x +5)

**What is the factorization formula?***2(x+y) = 2x +2y*- Variable is x
- So, 2x+2y together acts as an expression to the formula.
**What are the 6 types of factoring?***Greatest Common Factor.**Grouping.**The difference in Two Squares.**Sum or Difference in Two Cubes.**Trinomials.**General Trinomials.***What are the methods of factorization?***Factoring out the GCF.**The sum-product pattern.**The grouping method.**The perfect square trinomial pattern.**The difference of squares pattern.***What is the other name of the factorization method?***Doolittle’s method**.***What is the factorization method in the quadratic equation?****quadratic equations**.- Like
*ax2 + bx + c = 0.* - Solution for
:*r*.*r2 – 5r + 6 = 0* **What is the factorization of 72?**=*72*or*2 × 2 × 2 × 3 × 3*, where 2 and 3 are the*23 × 32***prime numbers**.

With the right steps under your garb, you now have a fair idea of **factorization** and its comparative factoring methods.

You can get on the right track and learn more with the **MSVGo app**, a video library that explains concepts with examples, explanatory visualizations, and animation for free.

With the aid of customized learning plans, it assists students in building confidence.

- Rational Numbers
- Linear Equations in One Variable
- Understanding Quadrilaterals
- Practical Geometry
- Data Handling
- Squares and Square Roots
- Cubes and Cube Roots
- Comparing Quantities
- Algebraic Expressions and Identities
- Visualizing Solid Shapes
- Mensuration
- Exponents and Powers
- Direct and Inverse Proportions
- Introduction to Graphs
- Playing With Numbers