## Precalculus (6th Edition) Blitzer

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 $3x^{4}y^{2}+3x^{2}y+9xy^{3}+12xy=3xy(x^{3}y+x+3y^{2}+4)$