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A
polynomial is a mathematical expression consisting of a finite set of
variables and constants, using only the arithmetic operations of
addition, subtraction and multiplication, and positive integer
exponents also. More precisely, it is an n-ary monomial, or a
sequence of addition and subtraction of integer powers of one or more
indeterminate variables.
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A
polynomial is an algebraic expression of the form:
P
(x) = an xn + an - 1 xn - 1 + n - 2 x n - 2 + ... + a1 x 1 + a 0
Being
an, an - 1 ... a1, ao numbers, called coefficients.
n
a natural number.
x
variable or indeterminate.
ao
is the intercept.
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Polynomials
is easy to work with because if you add, subtract or multiply the
result polynomials is another polynomial.
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The degree of a polynomial in one variable is the greatest exponent
of that variable.
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There are several types of polynomials, zero, homogeneous,
heterogeneous, complete, incomplete, tidy, equal and similar.
Zero
polynomial
It
is the polynomial that has all coefficients are zero.
P
(x) = 0x2 + 0x + 0
Homogeneous
polynomial
It
is the polynomial in which all terms or monomials are of the same
degree.
P
(x) = 2x2 + 3xy
Heterogeneous
polynomial
It
is the polynomial in which not all terms are not the same degree.
P
(x) = 2x3 + 3x2 - 3
Complete
polynomial
It
is one polynomial having all terms from the intercept to the term of
highest degree.
P
(x) = 2x3 + 3x2 + 5x - 3
Incomplete
polynomial
It
is the polynomial that has all terms from the intercept to the term
of highest degree.
P
(x) = 2x3 + 5x - 3
Ordered
polynomial
A
polynomial is ordered if the monomials that form are written in
greater or lesser degree.
P
(x) = 2x3 + 5x - 3
Same
polynomials
Two
polynomials are equal if verified:
The
two polynomials have the same degree.
The
coefficients of the terms of the same degree are equal.
P
(x) = 2x3 + 5x - 3
Q
(x) = 5x - 3 + 2x3
Such
polynomials
Two
polynomials are similar if verified with the same literal part.
P
(x) = 2x3 + 5x - 3
Q
(x) = 3x3 + 7x - 2
