# FACTORING COMMON MONOMIAL FACTOR

What is a Common Monomial Factor ?

A common monomial factor is a monomial that is a common factor to all of the terms of a polynomial expression.

Example of Monomial Expression :

8x5

Find the common monomial factor in monomial.

8x5 = 2x2 . 4x3

8x= 8x . x4

8x= 2x . 2x . 2x . x2

It gives as a product of two or more monomials.

Example of Binomial Expression :

3x4 - 6x2

Find the common monomial factor in binomial.

3x4 - 6x2

Take out the greatest common factor,

= 3x2(x2 - 2)

Here the Common Monomial Factor is 3x2

Example of Trinomial Expression :

15x4 - 10x3 + 5x2

Find the common monomial factor in Trinomial.

15x- 10x+ 5x2

Take out the greatest common factor,

5x2(3x2 - 2x + 1)

Here the Common Monomial Factor is 5x2

Another example of Trinomial Expression :

36x4y2 - 18x3y5 - 9x3y2

Find the common monomial factor in Trinomial.

36x4y- 18x3y5 - 9x3y2

Take out the greatest common factor,

= 9x3y2(4x - 2y3 - 1)

Here the Common Monomial Factor is 9x3y2

Factor out the greatest common monomial factor.

 Expressions1)  6x + 32)  24x2 - 8x3)  6x - 124)  2x2 + 8x5)  4x + 106)  10x2 + 35x7)  10x2y - 15xy28)  12x2 - 9x + 159)   3n3 - 12n2 - 30n10)  17x2 + 34x + 5111)  2x3 - 3x2 + 5x12) 13m + 26m2 - 39m3 Take Out GCF3(x + 2)8x(3x - 1)6(x - 2)2x(x + 4)2(2x + 5)5x(2x + 7)5xy(2x + 3y)3(4x2 - 3x + 5)3n(n2 - 4n - 10)17(x2 + 2x + 3)x(2x2 - 3x + 5)13m(1 + 2m - 3m2) Monomial Factor38x62x25x5xy33n17x13m

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