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POLYNOMIALS
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.
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.
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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