FACTOR OUT A MONOMIAL

The following steps will be useful to factor out a monomial from the given polynomial.  

Step 1 :

Find the greatest common factor of the terms in the polynomial given.  

Step 2 :

Divide each term by the greatest common factor and write the quotients inside the parentheses

Step 3 :

Write the greatest factor and parentheses together using multiplication. 

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 : 

12a- 21ab

Solution : 

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

Divide 12aand -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, 

12a- 21ab  =  3a(4a - 7b)

Example 3 :

Factor : 

6n- 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, 

6n- 3n5  =  3n3(2n - n2)

Example 4 :

Factor : 

10y- 9y2 + y

Solution : 

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

Divide 10yand -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, 

10y- 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 : 

-8m+ 24m6 + 12m5

Solution : 

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

Divide -8m7, 24m6 and 12mby 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, 

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

Example 7 :

Factor :

-7u2 - 21u3

Solution : 

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

Divide -7uand -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, -20m3nis 4m2n.

Divide 28m2n2, -12m3n, -20m3nby 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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