# About Polynomials

This is a mind map that contains information about the polynomials.

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Polynomials

Polynomials

A polynomial is a monomial or a sum ordifference of monomials. Since amonomial has only one term, that makesit the most simplest type of polynomial.

4x^2 would be an example of a polynomialbecause a polynomial does not haveexponents, roots, variables in thedenominator.

If a polynomial has two terms it will beclassified as a binomial. If it has threeterms it will be classified as a trinomial.

Finding Real Roots of Polynomial Equation

Factoring a polynomial equation can be away to find it's real roots. One can find thesolution or roots by using P(x) = 0, seteach factor equal to zero and solve for thex.

Depending on the equation, if it is aquadratic, one will first factor out thegreatest common factor then factorthe quadratic. Subsequently, set eachfactor equal to zero then solve for x.

Factoring Polynomials

If a number is divided by (x a), theremainder is the value of thefunctions a, if (x a) is a factor ofP(x), P(a) = 0.

Multiplying Polynomials

When multiplying polynomial by amonomial one must use the DistributiveProperty and Properties of Exponents.

Dividing Polynomials

When dividing multiplying polynomials onecause use long division. The steps arefirst to write the dividend in standardform including terms with thecoefficient of zero.

Curve Fitting with Polynomial Models

To make a mathematical model for adata given by a table, one will need tofigure out which function will beappropriate.

Finite Differences can help one identifythe degree of any polynomial data.

Something to help one find the degree

Transforming Polynomial Functions]

The transformations of f(x) are Verticaltranslation, Horizontal translation, Verticalstretch/compression, Horizontalstretch/compression, and Reflection.

The f(x) notation for a Verticaltranslation is f(x) + k. For a Horizontaltranslation the notation is f(x h). Af(x)for a Vertical stretch/compression.F(1/b x) for a Horizontalstretch/compression.

Investigating Graphs of Polynomial Functions

These functions are classified by thedegree of the polynomial.

Graphs of Polynomial Functions

Polynomial End Behavior Chart

Ex. P(x) = 4x^4 3x^2 + 5x + 6, The leading coefficient is 4, The degree is 3, which is odd., As x is infinity, P(x) is + infinity, and x is + infinity, P(x) is infinity.

Fundamental Theorem of Algebra

In the Fundamental Theorem ofAlgebra every polynomial function ofdegree n is greater or equal to 1 hasat least one zero.