A polynomial is an algebraic expression involving variables and constants that is formed using addition, subtraction, and multiplication, but not division. The degree of a polynomial refers to the highest power of the variable. Polynomials can be classified based on their number of terms as monomials (one term), binomials (two terms), or trinomials (three terms). They can also be classified based on degree as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), or of higher degrees. The number of zeros of a polynomial is equal to its degree.

2.  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.

3.  Degree of polynomial- The highest power
of x in p(x) is called the degree of the
polynomial p(x).
 EXAMPLE –
 f(x) = 3x +½ is a polynomial in the
variable x of degree 1.
 g(y) = 2y²  ⅜ y +7 is a polynomial in the
variable y of degree 2 .

4. On the basic of number of term.

5. 1. Monomial : Polynomial having only one term
e.g.= 4x, 8x etc.

6. 2. Binomial : Polynomial having two term
e.g. = 2x+6, 3x+4 etc.

7. 3.Trinomial : Polynomial having three
term
e.g. 2x-3x³+25, 4x³+2x²+1

8.  On the basic of degree.

9. 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+c
where 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. 2x
4
+
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

10. 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.