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About Polynomials

Polynomials
Polynomials
A polynomial is a monomial or a sum or
difference of monomials. Since a
monomial has only one term, that makes
it the most simplest type of polynomial.
4x^2 would be an example of a polynomial
because a polynomial does not have
exponents, roots, variables in the
denominator.
If a polynomial has two terms it will be
classified as a binomial. If it has three
terms it will be classified as a trinomial.
Finding Real Roots of Polynomial Equation
Factoring a polynomial equation can be a
way to find it's real roots. One can find the
solution or roots by using P(x) = 0, set
each factor equal to zero and solve for the
x.
Depending on the equation, if it is a
quadratic, one will first factor out the
greatest common factor then factor
the quadratic. Subsequently, set each
factor equal to zero then solve for x.
Factoring Polynomials
If a number is divided by (x a), the
remainder is the value of the
functions a, if (x a) is a factor of
P(x), P(a) = 0.
Multiplying Polynomials
When multiplying polynomial by a
monomial one must use the Distributive
Property and Properties of Exponents.
Dividing Polynomials
When dividing multiplying polynomials one
cause use long division. The steps are
first to write the dividend in standard
form including terms with the
coefficient of zero.
Fundamental Theorem of Algebra
In the Fundamental Theorem of
Algebra every polynomial function of
degree n is greater or equal to 1 has
at least one zero.
Investigating Graphs of Polynomial Functions
These functions are classified by the
degree 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.
Transforming Polynomial Functions]
The transformations of f(x) are Vertical
translation, Horizontal translation, Vertical
stretch/compression, Horizontal
stretch/compression, and Reflection.
The f(x) notation for a Vertical
translation is f(x) + k. For a Horizontal
translation the notation is f(x h). Af(x)
for a Vertical stretch/compression.
F(1/b x) for a Horizontal
stretch/compression.
Curve Fitting with Polynomial Models
To make a mathematical model for a
data given by a table, one will need to
figure out which function will be
appropriate.
Finite Differences can help one identify
the degree of any polynomial data.
Something to help one find the degree
183
author vip Study Smarter
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