Polynomial Functions - Revision history

Lila: /* Resources */

2021-10-21T18:59:02Z

Resources

Lila: Lila moved page Intro to Polynomial Functions to Polynomial Functions

2021-10-18T19:17:22Z

Lila moved page Intro to Polynomial Functions to Polynomial Functions

Lila: /* Resources */

2021-10-15T19:18:17Z

Resources

Lila at 19:17, 15 October 2021

2021-10-15T19:17:08Z

Lila: /* An example of a use of a polynomial equation */

2021-10-15T19:14:49Z

An example of a use of a polynomial equation

Lila: /* Example */

2021-10-04T16:57:41Z

Example

Lila at 16:57, 4 October 2021

2021-10-04T16:57:24Z

Lila at 16:56, 4 October 2021

2021-10-04T16:56:04Z

Lila at 15:29, 15 September 2021

2021-09-15T15:29:06Z

Johnraymond.yanez at 14:14, 17 August 2020

2020-08-17T14:14:48Z

← Older revision		Revision as of 18:59, 21 October 2021
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_FunctionsGN.pdf Guided Notes]
	* [https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA		* [https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA
		+
		+	== Licensing ==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikibooks.org/wiki/Algebra/Polynomials Polynomials, Wikibooks: Algebra] under a CC BY-SA license
		+	* [https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/FP1/Roots_of_Polynomial_Equations Roots of Polynomial Equations, Wikibooks: A-level Mathematics] under a CC BY-SA license

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 ==Resources==
 * [https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/FP1/Roots_of_Polynomial_Equations Roots of Polynomial Equations], Wikibooks: A-level Mathematics
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_Functions.pdf Intro to Power Functions and Polynomial Functions], Book Chapter
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_FunctionsGN.pdf Guided Notes]
 * [https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA

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 <math> 2(2x+1) </math>
 ==Resources==
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_Functions.pdf Intro to Power Functions and Polynomial Functions], Book Chapter
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_FunctionsGN.pdf Guided Notes]
 * [https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA

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 ===An example of a use of a polynomial equation===
-There is a story that in grade school the mathematician Gauss was asked to add the numbers 1 to 100 sequentially.  He is said to have intuited the sum could be expressed with the formula n(n+1)/2 and quickly gave the answer 5050.  The basis of this formula is that the numbers 1 through 49 added to the numbers 99 through 51 each yield 100.  It is interesting to look at how this formula works for the values 9 and 10.  For 10 we add the numbers 1+9, 2+ 8, 3+ 7, 4+ 6 to get 40 and we add the two remaining terms 5 and 10 to get 55.  For 9 we add the terms 1 + 8, 2 + 7, 3 + 6, 4+ 5 to get 4*9 = 36 + 9 = 45.  In the first case the n + 1 is the odd number and represents adding the 10 and the middle number, the 5.  In the second case the n is the odd number and the n+1 represents the sum for the preceding terms in the formula.  You may or may not find stories like this intriguing based on how your personality reacts to what is known as the [[w:Foundations of mathematics|foundational crisis of mathematics]].  Learning mathematics is a lot like learning a foreign language.  Some people seem more adept at learning languages than others, but with hard work learning a new language is something we can all do.
+There is a story that in grade school the mathematician Gauss was asked to add the numbers 1 to 100 sequentially.  He is said to have intuited the sum could be expressed with the formula n(n+1)/2 and quickly gave the answer 5050.  The basis of this formula is that the numbers 1 through 49 added to the numbers 99 through 51 each yield 100.  It is interesting to look at how this formula works for the values 9 and 10.  For 10 we add the numbers 1+9, 2+ 8, 3+ 7, 4+ 6 to get 40 and we add the two remaining terms 5 and 10 to get 55.  For 9 we add the terms 1 + 8, 2 + 7, 3 + 6, 4+ 5 to get 4*9 = 36 + 9 = 45.  In the first case the n + 1 is the odd number and represents adding the 10 and the middle number, the 5.  In the second case the n is the odd number and the n+1 represents the sum for the preceding terms in the formula.  You may or may not find stories like this intriguing based on how your personality reacts to what is known as the foundational crisis of mathematics.  Learning mathematics is a lot like learning a foreign language.  Some people seem more adept at learning languages than others, but with hard work learning a new language is something we can all do.
 ===Multiplying polynomials together ===

← Older revision		Revision as of 16:57, 4 October 2021
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	The greatest common factor between these terms is 2 because both of the terms can be divided by it and the coefficient and constant is still an integer. The example factored would become:		The greatest common factor between these terms is 2 because both of the terms can be divided by it and the coefficient and constant is still an integer. The example factored would become:
−

	<math> 2(2x+1) </math>		<math> 2(2x+1) </math>

← Older revision	Revision as of 19:17, 18 October 2021
(No difference)

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    When we express concepts like <math>y=x^2</math> the abstract behavior of what is being represented becomes a little harder to see.
-A '''monomial''' of one variable, let's say x, is an algabraic expression of the form
+A '''monomial''' (or '''power function''') of one variable, let's say x, is an algabraic expression of the form
 <div class="center"><math> c x^m \  </math> &nbsp;&nbsp;&nbsp; </div>

← Older revision		Revision as of 14:14, 17 August 2020
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−	[https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA	+	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_Functions.pdf Intro to Power Functions and Polynomial Functions], Book Chapter
		+	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_FunctionsGN.pdf Guided Notes]
		+	* [https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA