If the exponent of a variable in an algebraic expression is a whole number then
it is called a polynomial. A function p(x) of the form: p(x) = an x0 + a1 x + a2 x2
+ …. + an, where all a0 , a1, a2 , an are real numbers and n is non zero
negative number (i.e. a whole number) is called a polynomial.
For example : x + a, x2 – a2 + bx + c, x3 + 3x3 + 3x +1, z3 – 7y - 6 etc. are
polynomials. If the powers of variable x are either in increasing or decreasing
order, the polynomial in x is said to be in standard form.
The degree of a polynomial is the greatest exponent of that variable.
The degree of 2x + 5 is 1,
The degree of 3x2 + 7x - 6 is 2 and
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The degree of 6x5 – 3x2 y3 + 7xy2 is 5.
Polynomials of various degrees are:-
1. Linear polynomial: - have only one degree such as: - 3x + 5
2. Quadratic polynomial: - have at least two degree such as: - 3y2 – 7y + 6
3. Cubic polynomial: - have at least three degree such as: - 3x3 – 2x2 + 6x + 1
4. Bi quadratic polynomial: - have at least 4 degree such as: - x4 – 3x3 + 2x +
5x - 3
Number of terms in a polynomial:-
Monomial: - A polynomial containing one nonzero term. For example: - 5, 3x
Binomial: - A polynomial containing two nonzero terms. For example: - (3 + 6x),
(x - 5y)
Trinomial: - A polynomial containing three nonzero terms. For example: - (8 + 3x
+ x 2 ), ( 3y – 5xy + 7xy2 )
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