# Common Monomial Factor

How to factor a polynomial by using the common monomial factor of the terms: 2 examples and their solutions.

## ExampleFactor x^{3} + 3x

Solution

Solution (Detail)

First write the greatest common factor of

x^{3} and +3x:

x.

This x is the common monomial factor.

Write, x^{3}/x, x^{2} in the parenthesis.

Quotient of Powers

Write, +3x/x, +3 in the parenthesis.

So

x(x^{2} + 3)

is the answer.

## ExampleFactor a^{2} - 2ab + 4a

Solution

Solution (Detail)

First write the greatest common factor of

a^{2}, -2ab, and +4a:

a.

This a is the common monomial factor.

Write, a^{2}/a, a in the parenthesis.

Write, -2ab/a, -2b.

And write, +4a/a, +4 in the parenthesis.

So

a(a - 2b + 4)

is the answer.