# FACTOR OUT A MONOMIAL

## About "Factor out a monomial"

Factor out a monomial :

To factor out monomial, we need to follow the steps given below.

Step 1 :

First we have to find the greatest common factor each terms of the given polynomial.

Step 2 :

Then factor out the greatest common factor.

Let us see some example problems based on the above concept.

## Factor out monomial - Examples

Example 1 :

Factor out the greatest common factor

6 x⁴ + 4 x³ y

Solution :

Step 1 :

There are two terms 6 x⁴ and 4 x³ y in the given polynomial.

By finding greatest common factor, we get

6 x⁴   =  2 ⋅ 3 ⋅ x²⋅ x²

4 x³ y  =  2 ⋅ 2 ⋅ x²⋅ x ⋅ y

GCF  =  2x²

By writing the given as the multiple of 2x², we get

=  2x² (3x²) + 2x² (2xy)

Step 2 :

Factoring out the greatest common factor,

=  2x² (3x² + 2xy)

Example 2 :

Factor out the greatest common factor

15x³ + 10x²y - 25x²z

Solution :

Step 1 :

There are three terms,

First term  =  15x³   =  3 ⋅ 5 ⋅ x²

Second term  =  10x²y  =  2 ⋅ 5 ⋅ x² ⋅ y

Third term  =   - 25x² =  -5 ⋅ 5 ⋅ x² ⋅ z

GCF  =  5x²

By writing the given as the multiple of 2x², we get

=  5x² (3) + 5x² (2y) 5x² (-5x²z)

Step 2 :

Factoring out the greatest common factor,

= 5x²(3 + 2y - 5x²z)

Example 3 :

Factor out the greatest common factor

-7 u² - 21 u³

Solution :

Step 1 :

There are two terms,

First term  =  -7u² =  -7⋅ u²

Second term  =  - 21 u³  =  -3 ⋅ 7 ⋅ u² ⋅ u

GCF  =  -7u²

By writing the given as the multiple of -7u², we get

=  -7u² (1)  - 7u² (3u)

Step 2 :

Factoring out the greatest common factor,

= -7u²(1 + 3u)

Example 4 :

Factor out the greatest common factor

28 m²n² -12 m³n - 20 m³n²

Solution :

Step 1 :

In the given polynomial , there are three  terms,

First term  =  28 m²n²   =  4 ⋅ 7 ⋅ m² ⋅ n  n

Second term  =  -12 m³n  =  -4 ⋅ 3 ⋅ m² ⋅ m  ⋅ n

Third term  =  - 20 m³n²  =  -4 ⋅ 5 ⋅ m² ⋅ m  ⋅ n ⋅ n

GCF  =  4m²n

By writing the given as the multiple of 4m²n, we get

=  4m²n (7n) + 4m²n (-3m + 4m²n (-5mn)

Step 2 :

Factoring out the greatest common factor,

= 4m²n (7n- 3m - 5mn)

Example 5 :

Factor out the greatest common factor

12a²- 21 a b

Solution :

Step 1 :

In the given polynomial , there are three  terms,

First term  =  12a²  =  4 ⋅ 3 ⋅ a²

Second term  =  - 21 a b  =  -3 ⋅ 7 ⋅ a ⋅ b

GCF  =  3a

By writing the given as the multiple of 3a, we get

=  3a (4a) + 3a (-7b

Step 2 :

Factoring out the greatest common factor,

= 3a (4a - 7b) After having gone through the stuff given above, we hope that the students would have understood "Factor out a monomial".

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