 # Polynomials

## 02 Polynomials

#### POLYNOMIALS

Polynomial: Polynomial with variable x, is denoted by p(x) is expression of the type

are the coeeficients, and x is variable. ${\text{a}}_{\text{0}}$ is called constant term.

The polynomial $\text{p}\left(\text{x}\right)$ has terms.

e.g.

Monomials: A polynomial with one term is called monomial.

e.g

Binomial: A polynomial with two terms is called binomial.

e.g.

Trinomial: A polynomial with $\text{3}$ terms is called trinomial.

e.g.

Constant polynomial: Aconstant polynomial isa polynomial which is free of variable,and just contains a constant term

e.g.

Degree of polynomial: It is the highest power of variable in the expression of polynomial p(x).

The Polynomial has degree $\text{5}$.

Cubic polynomial: A polynomial with degree $\text{3}$ is called cubic polynomial.

e.g.

Quadratic Polynomial: A polynomial with degree $\text{2}$ is called Quadratic polynomial.

e.g.

Linearpolynomial : A polynomial with degree $\text{1}$ is called Linear polynomial.

e.g. 2x+4

Degree of constant polynomial is zero.

Value of polynomial:

Value obtained after replacing x by a real number k in the expression of $\text{p}\left(\text{x}\right)$ is called value of polynomial at .

For p(x)=

Put x=4

We get p(4) =

.

We say $\text{-7}$ is the value of polynomial at .

Zeroes of polynomial:The values of x, at which the polynomial p(x) is equal to 0 is called as zeroes of polynomial.

For e.g.

We get,

So $\text{11}$ is called zero of the given polynomial.

Remainder theorem:

When polynomial $\text{p}\left(\text{x}\right)$ is divided by polynomial , then the remainder will be p(a).

e.g.

If

Remainder=

Factor theorem:

For polynomial $\text{p}\left(\text{x}\right)$, if , then is factor of $\text{p}\left(\text{x}\right)$

e.g.For

so(x-3) is factor of .

Algebraic identities:

1)

2)

3)

4)

5)

5)

Or =

6)

Or =

7)

8)

9)