This is a mind map that contains information about the polynomials.
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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.
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.
When multiplying polynomial by amonomial one must use the DistributiveProperty and Properties of Exponents.
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.