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Polynomials

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Polynomials Galore!!!!

 

The following lens is a description of how to add, subtract, multiply and factor polynomials. The majority of the teaching is done through the use of videos. There are videos tutorials and examples. Be sure to scroll down or us the table of contents below to help you find the topic you are interested in. If you are a teacher check out my math teaching website.

Though I think this lens is valuable and can really help you understand polynomials sometimes it isn't enough. One of the most effective ways to learn math is one on one tutoring. Tutor.com offers 25 minutes for FREE and is something you should definitely check out.


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Mr. T. on the Web 

Square Roots
A lens showing how to simplify square roots.
Solving Inequalities
A lens showing how to graph and solve algebraic inequalities.
Linear Inequalities
Learn how to graph linear inequalities.
Quadratic Equations
A page showing how to solve quadratic equations.

Adding and Subtracting Polynomials 

There are two important things to remember about adding polynomials.

1) Add Like Terms - Like terms are monomials that have the exact same variable(s) with the exact same exponent(s). Like terms are combined by adding the coefficients.

2) Subtraction = Change All the Signs - If you are subtracting a polynomial then you change the subtraction to addition and then change all the signs of the polynomial that was being subtracted. For example:

(2x2 + 3x - 7) - (4x2 - 2x + 3)

Is rewritten as:

2x2 + 3x - 7 - 4x2 + 2x - 3

Notice how the parenthesis are removed after we deal with the subtraction.

The following video shows three examples how to add and subtract polynomials.

Don't Forget!!!

When you are subtracting polynomials you change ALL the signs of the terms in the paranthesis after the subtraction sign.

Adding/Subtracting Polynomials Example Set 1 

A110.8 Adding and Subtracting Polynomials

From http://www.squidoo.com/polynomials the following are a few examples of how to add or subtract polynomials. For more math help check out www.teachingandlearningmath.blogspot.com

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Multiplying Polynomials 

There are multiple different methods that are taught to students trying to learn how to multiply binomials together. FOIL, the smiley face method, and double distributive property are a few of them. All of these are valid ways to multiply binomials, but we are going to discuss double distributive property because it works for more difficult properties as well.

Double Distributive Property

The double distributive property describes the process of multiplying two binomials together. It works like this:

1) Multiply the first term of the first binomial times the two terms of second binomial.

2) Multiply the second term of the first binomial times the two terms in the second binomial.

3) Add like terms.

The good thing about learning it this way is that it is easy to extend the method to more complex problems. For example if you are multiplying two trinomials:

1) Multiply the first term of the first trinomial times all three terms in the second trinomial.

2) Multiply the second term of the first trinomial times all three terms in the second trinomial.

3) Multiply the third term of the first trinomial times all three terms in the second trinomial.

4) Add like terms.

The following videos show examples of multiplying various polynomials together.

Multiplying Binomials Example 1 

A110.3 Multiplying Polynomials

From http://www.squidoo.com/polynomials the following is an example of how to multiply two binomials together. For more math help check out www.teachingandlearningmath.blogspot.com

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Multiplying Binomials Example 2 

A110.4 Multiplying Polynomials Special Cases

From http://www.squidoo.com/polynomials the following are special case examples of how to multiply binomials. For more math help check out www.teachingandlearningmath.blogspot.com

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Multiplying Binomials Example Set 3 

A110.5 Multiplying Binomials

From http://www.squidoo.com/polynomials the following is an example of how to multiply polynomials. For more math help check out www.teachingandlearningmath.blogspot.com

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Multiplying Binomials Example Set 4 

A110.6 Multiplying Binomials

From http://www.squidoo.com/polynomials the following is a video example of how to multiply to binomials together. For more math help check out www.teachingandlearningmath.com

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Multiplying a Binomial times a Trinomial 

A110.7 Multiplying Polynomials

From http://www.squidoo.com/polynomials the following is an example of how to multiply polynomials. For more math help check out www.teachingandlearningmath.blogspot.com

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Factoring Quadratic Expressions 

As with multiplying binomials there are various methods for factoring quadratic equations. The following videos illustrate the "guess and check" method of factoring quadratics. I like to teach this method because it helps students understand the "why" of factoring. The other methods are more "magic" and don't teach as much for understanding.

The only special case I teach is the difference of two squares. There are a couple of examples of how that works as well.

Factoring Quadratics Example Set 1 

A110.9 Factoring Quadratic Expressions

From http://www.squidoo.com/polynomials the following are a couple of examples of how to factor quadratic equations. For more math help check out www.teachingandlearningmath.blogspot.com

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Factoring Quadratic Equations Example Set 2 

A110.10 Factoring Quadratic Expressions

From http://www.squidoo.com/polynomials the following are a couple of video examples of how to factor quadratics. For more math help check out www.teachingandlearningmath.blogspot.com

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Factoring Quadratic Expressions Example Set 3 

A110.11 Factoring Quadratic Expressions

From http://www.squidoo.com/polynomials the following are two examples of how to factor quadratic expressions. For more math help check out www.teachingandlearningmath.blogspot.com

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Factoring Quadratic Expressions Example Set 4 

A110.12 Factoring Quadratic Expressions

From http://www.squidoo.com/polynomials the following are two examples of factoring quadratic expressions. For more math help check out www.teachingandlearningmath.blogspot.com

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Factoring Quadratic Expressions Example Set 5 

A110.13 Factoring Quadratic Expressions

From http://www.squidoo.com/polynomials the following are two examples of how to factor quadratic expressions. For more math help check out www.teachingandlearningmath.blogspot.com

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Let me know what you think of this lens... 

I would love to hear how you would teach these topics or what you got from this lens.

ElizabethJeanAllen

I don't teach students how to work with polymomials. We balance equations and calculate half-lifes. I wish I was an angel so I could bless you. We teachers need all the help we can get. * * * * *
Liz

Posted April 07, 2008

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MrT68

About MrT68

My name is Trent Tormoehlen and I am a math teacher at Sycamore School in Indianapolis Indiana.  I will also be helping coach the schools Math Counts team. It is my goal to create the best free online math help possible. 

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