FACTOR OUT A MONOMIAL

Example 1 :

Factor :

6x⁴ + 4x³y

Solution : 

Greatest common factor of 6x⁴ and 4x³y is 2x³. 

Divide 6x⁴ and 4x³y by 2x³.

6x⁴/2x³  =  3x

4x³y/2x³  =  2y

Write the quotients 3x and 2y inside the parenthesis and multiply by the greatest common factor 2x³.

2x³(3x + 2y)

So, 

6x⁴ + 4x³y  =  2x³(3x + 2y)

Example 2 :

Factor : 

12a² - 21ab

Solution : 

Greatest common factor of 12a² and -21ab is 3a. 

Divide 12a² and -21ab by 3a. 

12a²/3a  =  4a

-21ab/3a  =  -7b

Write the quotients 4a and -7b inside the parenthesis and multiply by the greatest common factor 3a.

3a(4a - 7b)

So, 

12a² - 21ab  =  3a(4a - 7b)

Example 3 :

Factor : 

6n³ - 3n⁵

Solution : 

Greatest common factor of 6n³ and -3n⁵ is 3n³. 

Divide 6n³ and -3n⁵ by 3n³. 

6n³/3n³  =  2n

-3n⁵/3n³  =  -n²

Write the quotients 2n and -n² inside the parenthesis and multiply by the greatest common factor 3n³.

3n³(2n - n²)

So, 

6n³ - 3n⁵  =  3n³(2n - n²)

Example 4 :

Factor : 

10y³ - 9y² + y

Solution : 

Greatest common factor of 10y³, -9y² and y is y. 

Divide 10y³ and -9y² and y by y. 

10y³/y  =  10y²

-9y²/y  =  -9y

y/y  =  1

Write the quotients 10y², -9y and y inside the parenthesis and multiply by the greatest common factor y.

y(10y² - 9y + 1)

So, 

10y³ - 9y² + y  =  y(10y² - 9y + 1)

Example 5 :

Factor :

15x³ + 10x²y - 25x²z

Solution : 

Greatest common factor of 15x³, 10x²y, -25x²z is 5x².

Divide 15x³, 10x²y and -25x²z by 5x².

15x³/5x²  =  3x

10x²y/5x²  =  2y

-25x²z/5x²  =  -5z

Write the quotients 3x, 2y and -5z inside the parenthesis and multiply by the greatest common factor 5x².

5x²(3x + 2y - 5z)

So, 

15x³ + 10x²y - 25x²z  =  5x²(3x + 2y - 5z)

Example 6 :

Factor : 

-8m⁷ + 24m⁶ + 12m⁵

Solution : 

Greatest common factor of -8m⁷, 24m⁶ and 12m⁵ is 4m⁵. 

Divide -8m⁷, 24m⁶ and 12m⁵ by 4m⁵. 

-8m⁷/4m⁵  =  -2m²

24m⁶/4m⁵  =  6m

12m⁵/4m⁵  =  3

Write the quotients -2m², 6m and 3 inside the parenthesis and multiply by the greatest common factor 4m⁵.

4m⁵(-2m² + 6m + 3)

So, 

-8m⁷ + 24m⁶ + 12m⁵  =  4m⁵(-2m² + 6m + 3)

Example 7 :

Factor :

-7u² - 21u³

Solution : 

Greatest common factor of -7u² and -21u³ is -7u².

Divide -7u² and -21u³ by -7u².

-7u²/(-7u²)  =  1

-21u³/(-7u²)  =  3u

Write the quotients 1 and 3u inside the parenthesis and multiply by the greatest common factor -7u².

-7u²(1 + 3u)

So, 

-7u² - 21u³  =  -7u²(1 + 3u)

Example 8 :

Factor :

28m²n² - 12m³n - 20m³n²

Solution : 

Greatest common factor of 28m²n², -12m³n, -20m³n² is 4m²n.

Divide 28m²n², -12m³n, -20m³n² by 4m²n.

28m²n²/4m²n  =  7n

-12m³n/4m²n  =  -3m

-20m³n²/4m²n  =  -5mn

Write the quotients 7n, -3m and -5mn inside the parenthesis and multiply by the greatest common factor 4m²n.

4m²n(7n - 3m - 5mn)

So, 

28m²n² - 12m³n - 20m³n²  =  4m²n(7n - 3m - 5mn)

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