A monomial is a number, a variable or a product of a number and
a variable where all exponents are whole numbers. That means
that
all are examples of monomials whereas
are not since these numbers don't fulfill all criteria.
The degree of the monomial is the sum of the exponents of all
included variables. Constants have the monomial degree of 0.
If we look at our examples above we can see that
Monomial

Degree

42

0

5x

0 + 1 = 1

14x^{12}

0 + 12 = 12

2pq

0 + 1 + 1 = 2

A polynomial as oppose to the monomial is a sum of monomials
where each monomial is called a term. The degree of the polynomial
is the greatest degree of its terms. A polynomial is usually
written with the term with the highest exponent of the variable
first and then decreasing from left to right. The first term of a
polynomial is called the leading coefficient.
Polynomial just means that we've got a sum of many monomials. If
we have a polynomial consisting of only two terms we could instead
call it a binomial and a polynomial consisting of three terms can
also be called a trinomial.
We can add polynomials. We just add the like terms to combine
the two polynomials into one.
Example:
Begin by grouping the like terms and then just simplify the
expression
The same goes for subtracting two polynomials. Just subtract the
like terms Or in other words add its opposites. Make the two
polynomials into one big polynomial by taking away the parenthesis.
Don't forget to reverse the signs within the second parenthesis
since your multiplying all terms with 1.
Multiplication of polynomials is based on the distributive
property.
When you multiply polynomials where both polynomials have more
than one term you just multiply each of terms in the first
polynomial with all of the terms in the second polynomial.
When multiplying two binomial you can use the word FOIL to
remember how to multiply the binomials. FOIL stands for
First, Outer,
Inner, Last.
Video lesson: Simplify the following
expression