Polynomials are algebraic expressions involving whole number exponents of a variable. There are several types of polynomials based on the number of terms: monomials have one term, binomials have two terms, and trinomials have three terms. Polynomials are also classified based on degree, which is the highest exponent of the variable. The degree determines whether a polynomial is constant, linear, quadratic, cubic, etc. Quadratic polynomials, which have a degree of two, can have zero, one, or two zeros depending on whether their graph crosses the x-axis. Parabolas represent the graphs of quadratic functions.

1. What are
POLYNOMIALS

2. Polynomial It is an algebraic expression in which the
power of the variable is a whole number.
Polynomial
poly means many. nomial means term

3. Monomial A monomial is a polynomial
having only one terms.
Binomial A binomial is a polynomial having
only two terms.
Trinomial A trinomial is a polynomial
having only three terms.
Types of polynomial on the basis of terms

4. Degree of the polynomial It is the highest
exponential power of the polynomial.
Types of polynomial on the basis of degree
Constant polynomial polynomial that have the
degree zero called constant polynomial.
For example 2x0
Zero polynomial polynomial having value zero
For example 0x100

5. Linear polynomial polynomial that have degree one
Called linear polynomial
For example 2x+3
● It has maximum 2 terms
● It has minimum 1 term
Quadratic polynomial polynomial that have degree
two called quadratic polynomial
For example 2x2+3
● It has maximum 3 terms
● It has minimum 1 term

6. Cubic polynomial polynomial that have degree 3
called cubic polynomial
For example 2x3+6x2+4x+6
● It has maximum 4 terms
● It has minimum 1 term
● Linear polynomial can have only one zero
● Quadratic polynomial can have only two zeroes
● Cubic polynomial can have only three zeroes

7. Case1: Here,the graph cuts x-axis at two distinct
points A and A’
therefore, quadratic polynomial
has two zeroes.

8. Case2: Here,the graph cuts the x-axis at
exactly one point, i.e.,at two coincident points.
So,the two points A and A’of case1 coincide here
to become one point A. Therefore, quadratic
polynomial has one zero .

9. Case3: Here,the graph is either completely above
the x-axis or completely below the x-axis.
So,it does not cut the x-axis at any point
Therefore, quadratic polynomial has no zero.

10. Parabola
A parabola is U-shaped curves that
is drawn for quadratics function ,
f(x) =ax^2+bx+c .Parabola is of two
shapes either open upward or curved
downward.
X 1 2 3 -1 -2 -3
Y 4 11 22 2 7 16

14. Some Formulae