Polynomial

POLYNOMIALS

Definition of Polynomial

An algebraic expression that has only whole numbers as the exponents of the variables, called a Polynomial

What is algebraic expression ?
When variables and constant term with some or all the operators + , - , ÷ , x.

What is Whole numbers ?
All counting numbers with zero. i.e. 0,1,2,3,4,5,...

You understand Exponent term ?
Exponent means raise to the power of...

VARIABLE
A term which can take any real value, according to situation is called VARIABLE.
Its value can keep changing. Generally denoted by x, y, z, etc.

CONSTANT
A term that's value remains same at any situation. Generally denoted by a, b, c, etc.
eg. 2x, 3x/2, -7x, etc. each expressions like ax.
where x is variable and a is constant.

NOTE: An algebraic expression will not be a polynomial if it contains:
i) Fractional exponent
ii) Negative exponent

eg. i) 2x²+4x+1
polynomial in variable x,
Three term,
Coefficient of x² is 2
Coefficient of x is 4
constant term = 1

eg. ii) x½+2
Above expression is not a polynomial because the exponent of x is ½
i.e. Rational

eg. iii) x^-2 + x + 1
Above expression is not a polynomial because the exponent of x is -2.
i.e. Negative

Classification of Polynomial on the basis of term

MONOMIAL
A Polynomial which have only one term is called a monomial.
eg. 5x, -3x², x², etc.

BINOMIAL
Which have only 2 term is called a binomial.
eg. x-2, x²+x, y²+5, etc.

TRINOMAIL
Which have only 3 term is called a trinomial.
eg.x²+x+2, x^4+x-2, x^9+6x²+5,etc.

Classification of Polynomial

LINEAR POLYNOMIAL
Whose degree 1 is called a Linear polynomial.
eg. 2x+3,2x,x,...etc.
General form : ax+b where a≠0

QUADRATIC POLYNOMIALWhose degree 2 is called a Quadratic polynomial.
A word 'Quadrate' which means 'Square'.
eg. 4x²+6x+6
General form : ax²+bx+c where a≠0

CUBIC POLYNOMIALWhose degree 3 is called a Cubic polynomial
eg. x³+2x²+x+4
General form : ax³+bx²+cx+d where a≠0