## FACTOR MONOMIALS

Factor monomials :

To factor a polynomial, first find the greatest common factor (GCF) of each monomial. Then factor out the geatest common factor using the distributive property.

Example 1 :

Factor out the greatest common factor.

9 g³– 6 g²

Solution :

9 g³ = 3 xx x g x g

– 6 g² = -1 x 2 x 3 x x g

Greatest common factor of 9 g³ and – 6 g² is x g x g = 3 g²

Now factor out g² from both terms, we get

=  g² x g + g² (-2 g)

=  g² (3 g - 2)

Hence the factored form of the polynomial is

g² (3 g - 2)

Example 2 :

Factor out the greatest common factor.

2 c + 4 c²

Solution :

2 c  = 2 x 1 x c² x c²

4 c² = 2 x 2 x c²

In both terms we can find 2 c². So the greatest common factor is 2 c²

Write both terms as the multiple of 2 c²

=  2 c² c² +  2 c² c²

By factor out 2 c² from both terms, we get

=  2c² (c² + 2)

Hence the factored form of the polynomial is

2c² (c² + 2)

Example 3 :

Factor out the greatest common factor.

6 x + 10 x

Solution :

6 x = 2 x x x x x x x x x

10 x = 2 x 5 x x

In both terms we can find 2 x. So the greatest common factor is 2 x

Write both terms as the multiple of 2x

=  2 x 3 x³ + 2 x x 5

By factor out 2 x from both terms, we get

=  2 x (3 x³ + 5)

Hence the factored form of the polynomial is

2 x (3 x³ + 5)

Example 4 :

Factor out the greatest common factor.

8 t + 22

Solution :

8 t = 2 x 2 x 2 x t

22 = 2 x 11

In both terms we can find 2. So the greatest common factor is 2

Write both terms as the multiple of 2

=  2 4t + 2 x 11

By factor out 2 from both terms, we get

=  2 (4t + 11)

Hence the factored form of the polynomial is

2 (4t + 11)

After having gone through the stuff given above, we hope that the students would have understood "Factor monomials".

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