#### Answer

A polynomial is a sum of terms (monomials), each of the form:
(constant)(power of a variable)(power of a variable)...(power of a variable)
such as $3x^{2}y$ ( a monomial)
An example of a polynomial is:
$3x^{4}y^{2}+3x^{2}y+9xy^{3}+12xy$
Each term contains a multiple of 3, a nonzero power of x, and a nonzero power of $y$.
The greatest common factor (gcf) is a term that contains
- the greatest factor of all the constants, and
- the greatest power of each variable, appearing in all the monomials.
In our example, the gcf is $3xy$, and we can write
$3x^{4}y^{2}+3x^{2}y+9xy^{3}+12xy=3xy(x^{3}y+x+3y^{2}+4)$

#### Work Step by Step

Given above.