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Types Of Polynomials

Types of Polynomials Assignment / Homework Help
DEFINITION:

A polynomial in one variable x is an algebraic expression in x of the form:

p(x) = anxn + an-1xn-1 + an-2xn-2 + ... + a2x2 + a1x + a0 ,

where a0, a1, a2, ...., an are constants and an ≠ 0.

n is called the degree of the polynomial which has to be a whole number.

a0, a1, a2, ...., an are the coefficients of X0, X1, X2, ...., Xn xn respectively. For example, in a polynomial 5x2 + 3x -1, the coefficient of X2 is 5, the coefficient of x is 3 and -1 is the coefficient of X0.

Each anxn, an-1xn-1, ..., a0 is called a term of the polynomial p(x). For example, in x2 + 2 there are two terms x2 and 2, in 4x2 + 2x + 3 there are 3 terms 4x2, 2x and 3.


TYPES OF POLYNOMIALS:

MONOMIAL:

Polynomials which have only one term are known as monomials. For example, 5x, 3x3, 4x2, y and 6 all are monomials because they have only one term.

BINOMIAL:

Polynomials which have only two terms are termed as binomials. For example, x3 x2, x + 2, y4 + 1, u23 u3 are all binomials as they contain only two terms.

TRINOMIAL:

Polynomials having only three terms are named as trinomials. A few examples of trinomials are given below:

p(x) = x + x2 5

q(x) = √3 - x + x3

r(y) = y4 + y + 3

All the above polynomials are trinomials because all of them contain only 3 terms.

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