Polynomials Homework Help
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Polynomials
A mathematical expression contains constants, variables and non-negative integer exponents, that can be combined by using the basic mathematical expressions like addition, subtraction and multiplication but not division by a variable is called polynomial. In Greek, “Poly” means ‘many’ and in Latin “nomial” means ‘terms’. Thus, it is defined as an expression with many terms.
Note that, a term includes one or more variables raised to the non-negative
integer power and multiplied by a constant co-efficient. The term includes
only a constant is called constant term. Moreover, it is not possible to
have infinite number of terms in a polynomial.
Polynomial function:
If there is only one variable involved in a polynomial, then it is named as
a polynomial function. The general form of a polynomial function is as
follows:
Where
c0,
c1,…cn-1,cn is a constants in R and
n
is a non-negative integer.
Note that,
c0xn+c1xn-1+…+cn-1x+cn is a one-variable polynomial.
Examples:
1. Consider 2
x2+3
y+2. Here the number of terms is 3.
Variables are
x,y whose highest degree, 2. It is a polynomial.
2. Consider –4
x2+5
y–3+2. Here, the number of terms is 3.
Variables are
x,y in which
y has a negative exponent. It
is not a polynomial.
3. Consider
. Here, the number of terms is 3. Variables are
x,y in which
y has a fractional exponent. It is not a polynomial.
4. Consider
. Here, the number of terms is 3. Variables are
x,y with one
variable is a division of another variable. It is not a polynomial.
Types of polynomial:
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