This is a free lesson from our course in Algebra I
In this lesson you'll go through the basics of a monomial, polynomial and the degree of a polynomial, as simply
as possible and with the help of a number of examples. Some of the basic points
in this lesson are mentioned below. Not that this might seem complicated here in
text, but once you have instructor explain it to you in their voice and handwriting
in the video above, it will be easy to follow. (More text below video...)
(Continued from above) Here are some of the basics for you to keep in
mind:
• 'monomial' refers to a polynomial that has only a single (mono) term and the product of multiplying monomials together also results in a monomial
e.g. x, 2x, xy, (10xy^{4})/3 • 'polynomials'
refer to mathematical expressions that contain multiple terms x + 5, 2x
 5, (5xyz^{3})/4 + 7x etc • the degree of a term is the sum of the powers of each variable in
the term. For example, the polynomial 5x^{4} + 2x^{3}
 x + 7 has four terms. The first term has a degree of 4, the second term
has a degree of 3, the third term has a degree of 1, and a last term has a degree
of 0
• when a polynomial is expressed as a sum or difference of terms, the term with the
highest degree, is the degree of the polynomial. Therefore, the polynomial has a
degree of 4 which is the highest degree of any term
• while adding or subtracting polynomials, remember that you can only combine
like terms. 'Like terms' contain the sample variables and differ by the numeric
coefficient in the left, e.g. 4x and 6x
are like terms, and can be added to get 10x
• multiplying polynomials is a little more complicated, and involves adding up the
products of multiplying each term in the first polynomial by each term in the second
polynomial. The lesson also explains the concept of 'FOIL', which is short form of "First, Outside, Inside, Last"
and refers to which terms you multiply together and add up when multiplying two
polynomials, each composed of two monomials. Again, this may appear little complicated
here in text, but it will be easy to follow once you hear the instructor explain
it in the video below.
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