This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started.

In this mini-lesson we cover 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, it will be easy to follow. Here are some of the basics for you to keep in mind:

In this mini-lesson we cover 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, it will be easy to follow. 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 same 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 mini-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.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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- Mathematics > Algebra
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