polynomials

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by NicoMingrone
Last updated 4 years ago

Discipline:
Math
Subject:
Number Operations

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polynomials

To classify polynomials you use the number of terms in the polynomial, you can also use the leading coefficient. ( the polynomial must be in standard form to do this)0= constant1=linear2=quadratic3=cubic4=quartic5= quintic

polynomials ( ' all their awesomeness)

classifying by terms1=monomial2=binomial3=trinomial4+=polynomial

GRAPHIN'The end behaviour of a graph can be easily determined by the leading value, namely the parity of the degree ' the polarity of the coefficient, as evidenced by this chart.

CONTRIBUTORSWilliam Downs, 16Enjoys: Reading, Cats, ' the cold. Dislikes: Tomatoes,direct sunlight.Nico Mingrone, 16Enjoys: drawing, reading and playing videogames and dogsDislikes: not being able to go on walks, siblings on most days

In essence, graphing a polynomial is all about finding zeros, which is done primarily by factoring the polynomial and solving for x by making the resulting equations equal to zero.

SPECIALSa2+2ab+b2=(a+b)2a2-2ab+b2=(a-b)2a2-b2=(a+b)(a-b)a3+b3=(a+b)(a2-ab+b2)a3-b3=(a-b)(a2+ab+b2)

Though there are many equations based on the structure of the poynomial to solve for max and minimum (c - b2/4a), the simplest way is, of course, to punch the equation into one of these.

LONGtake the monomial and put the rest of the problem in the divison box and multiply the x to get the term you want

NOTES ON STANDARDIZATIONZeros: 0,-3,61. Use zeros to create a factored form y=x(x+3)(x-6)2. Multiply y=x(x2-3x-18)3. Distribute y=x3-3x2-18x4. Celebrate *\(^O^)/*

THE HARD WAYGood luck.

FACTORING:If the polynomial's terms all share a term or there is a specific term that fits into them all, then factor it out. y=2x3+10x2-20xbecomesy=2x(x2+5x-10)from there, there are a few options.

Let it also be known that by finding these zeros, you have soved the polynomial.

THE EASY WAYIf there exists factors of the last values that add up to the middle value, such as in the case of x2+6x+8, the you replace that middle value with those two factors. Doing this will create a four-value polynomial, which you can then divide into two binomials ' factor.

Additionally, for a more accurate graph, one can plug in values for x to find at what y value the graph meets that point.

DIVISION

SYNTHETICyou take the nuumber with the x and take the opposite then take the first number multiply it by it by the x number and add it to the next

This guy explains it better than we have...

...but these kids explain it far funkier than him.


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