A polynomial is an expression made with constants, variable and exponent which are combined using addition, subtraction and multiplication but not division.

The exponents can only be 0,1,2,3……etc.

Degree of polynomial- The highest powerof x in p(x) is called the degree of thepolynomial p(x).

EXAMPLE –

f(x) = 3x +½ is a polynomial in thevariable x of degree 1.

g(y) = 2y² ⅜ y +7 is a polynomial in thevariable y of degree 2 .

On the basic of number of term.

1. Monomial : Polynomial having only one term

e.g.= 4x, 8x etc.

2. Binomial : Polynomial having two term

e.g. = 2x+6, 3x+4 etc.

3.Trinomial : Polynomial having three term

e.g. 2x-3x³+25, 4x³+2x²+1

On the basic of degree.

i) Constant polynomial –

polnomials having degree 0. e.g. 32, -

5.

ii) Linear polynomial – polynomials

having degree 1. e.g. x+5, 6x-3

The general form is ax+b. where as a is not equal to 0.

ii) quadratic polynomial –polynomials having degree 2. e.g.

2x² + 3x -8.

The general form is ax²+bx+cwhere as a is not equal to 0.

iii) Cubic polynomial – polynomials

having degree 3. e.g. 6x³ + 7x² -x-6.

The general form is ax³+bx²+cx+d where as a is not equal to 0

v) bi-quadratic polynomial- polynomials having degree 4. e.g. 2x4

+

x³ - 8x² +5x -8.

The general form is ax +bx³+cx²+dx+e where as a is not equal to 0.

On the basis of degree

A real number α is a zero of a polynomial f(x), if f(α) = 0.

e.g. f(x) = x³ - 6x² +11x -6

f(2) = 2³ -6 X 2² +11 X 2 – 6

= 0 .

Hence 2 is a zero of f(x).

The number of zeroes of the polynomial is the degree of the

polynomial. Therefore a quadratic polynomial has 2 zeroes and cubic

3 zeroes.