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View the video. While watching, work out the problems in your composition notebook.

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View the video. While watching, work out the problems in your composition notebook.

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WatchKnowLearn - Free K-12 educational videos

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Free K-12 educational videos ... organized. Tens of thousands of excellent, educational videos in a huge, intuitive directory. Organized, reviewed, rated, and described by teachers. Ideal as a supplement to a curriculum or for independent study. Designed for teachers, students, parents, homeschoolers, educators ... and all life-long learners!

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View the video. While watching, work out the problems in your composition notebook.

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Factoring and Using the Distributive Property

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Read through the following information. Then, post a 2-4 sentence summary of what you learned. Post to our Padlet.

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A polynomial looks like this:

example of a polynomial
this one has 3 terms

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

A polynomial can have:

that can be combined using addition, subtraction, multiplication and division ...

... except ...

So:

A polynomial can have constants, variables and exponents,
but never division by a variable.

Also they can have one or more terms, but not an infinite number of terms.

Polynomial or Not?

These are polynomials:

(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

These are not polynomials

3xy⁻² is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

2/(x+2) is not, because dividing by a variable is not allowed

1/x is not either

√x is not, because the exponent is "½" (see fractional exponents)

x/2 is allowed, because you can divide by a constant

also 3x/8 for the same reason

√2 is allowed, because it is a constant (= 1.4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:
How do you remember the names? Think cycles!

There is also quadrinomial (4 terms) and quintinomial (5 terms),
but those names are not often used.

Variables

Polynomials can have no variable at all

Example: 21 is a polynomial. It has just one term, which is a constant.

Or one variable

Example: has three terms, but only one variable (x)

Or two or more variables

Example: has two terms, and three variables (x, y and z)

What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.

For example we know that:

So you can do lots of additions and multiplications, and still have a polynomial as the result.

Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.

You can also divide polynomials (but the result may not be a polynomial).

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

You don't have to use Standard Form, but it helps.

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A polynomial looks like this: example of a polynomial this one has 3 terms Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms" A polynomial can have: that can be combined using addition, subtraction, multiplication and division ... ... except ...

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Work through the following in your composition notebook. Then, write a 2-4 sentence summary explaining how to multiply polynomials. Post to our Padlet.

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Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Enjoy! Then write one paragraph (8-10 sentences) explaining which game you chose and what you learned from it. Post to our Padlet.

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Cool math Algebra Help Lessons: Polynomials

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Algebra polynomals lessons with lots of worked examples and practice problems. Very easy to understand!

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After choosing an Avatar (pic), record a 2-3 minute summary of what you have learned about polynomials. Post your Blabber to our Padlet.

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Choose your games to play and review.

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ClassTools Arcade Game: "Algebra Questions"

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Classtools.net Home | Premium Login | Facebook Fanpage | PowerSearch | Contact

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Create two polynomials to multiply and show your work below. Then provide your reflection of what you have learned by answering the following questions:
1.) What misconception did you get corrected today?
2.) What new information did you gain in today's lesson?
3.) What did you learn you are more or now confused about?