The concept of adding a monomial to another monomial making it two monomials
which is otherwise called ‘binominal’ needs to be explained so that the child can
understand trinominal, polynominal, etc., easily.
- Trinomial
An algebraic expression with three terms is said to be a trinomial.
Eg. : x + 2y - 3z, - 2x + 7y - 9z, 2xy - 3yz - 8 zx are all trinomials as they all
contain three algebraic terms.
- Polynomial
A function P(x) of the form, P(x) =a 0 + a 1 x + a 2 x^2 + a 3 x^3 + .....+ anxn where a 0 ,a 1 ,a 2 ,a 3 ,...,an
are real numbers and ‘n’ is a non-negative integer, is called a polynomial in ‘x’ with
real coefficients. To state in simple terms, an algebraic expression having four or
more terms is called a polynomial. It is customary to denote a polynomial as P(x).
Eg. : P(x) = x^3 + x^2 - x - 5
Here the algebraic expression contains four terms and hence it is called a polynomial.
In fact, polynomial is a generic term denoting all the algebraic expressions. A
polynomial with a single term is called as monic polynomial or a monomial, and the
idea is same for expressions containing higher number of terms also.
If more than one polynomial are to be dealt with at the same time, then they can be
denoted as Q(x) and R(x) also.
With the description of monomial, binominal and trinomial, the child will be able to
understand the concept of polynomial easily.
- Degree of a Polynomial
The exponent in the term with the highest power is the degree of the polynomial.
In general, if anxn + an-1xn-1 + ...+ a 0 is a polynomial, an^ ≠ 0, then ‘n’ is the degree of
the polynomial.
