**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 **x** 3 **x** g **x** g **x** g

– 6 g² = -1 x 2 **x** 3 **x** g **x** g

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

Now factor out 3 g² from both terms, we get

= 3 g² **x **3 g + 3 g² **x **(-2 g)

= 3 g² (3 g - 2)

Hence the factored form of the polynomial is

3 g² (3 g - 2)

**Example 2 :**

Factor out the greatest common factor.

2 c⁴ + 4 c²

**Solution :**

2 c⁴ = 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 **x **c² + 2 c² **x **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 x⁴ + 10 x

**Solution :**

6 x⁴ = 2 **x** 3 **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 **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 **x **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".

Apart from the stuff given above, if you want to know more about "Factor monomials", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

- Factor quadratics
- Factor quadratic equation whose leading coefficient is not equal to 1
- Factor using a quadratic pattern
- Factor by grouping
- Factor sums and differences of cubes
- Factor polynomials
- Factor polynomials using algebraic identities

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