# Polynomials Class 9 Notes Maths - Chapter 2

## Chapter: 2

## What Are Polynomial ?

## Meaning Of A Polynomial

- Polynomial is an algebraic expression, where variables have only whole numbers as an exponent.

Like x^{2}– y^{2}+ 2xy, x^{2}+ 2, etc. - A polynomial in one variable, say x, is an algebraic expression of the form P(x) = a
_{n}x^{n}+ a_{n-1}x^{n-1}+.......a_{2}x^{2}+ a_{1}x + a_{0}, where a_{0}, a_{1}, a_{2},.......,a^{n are constants and respectively known as coefficients of x0, x, x2......., xn.}

## Terms Of A Polynomial

If a polynomial p(x) = a

_{n}x^{n}+ a_{n-1}x^{n-1}+ ..... + a_{2}x^{2}+ a_{1}x + a_{0}, then each of a_{n}x^{n}, a^{n-1}x^{n-1},......, a_{0}is called a term of the polynomial p(x).## Degree Of A Polynomial

## Types Of Polynomials

**According to Number of Terms:**

- Polynomials having only one term are called monomials.
- Polynomials having only two terms are called binomials.
- Polynomials having only three terms are called trinomials.

**According to Degree:**

- A polynomial of degree 0 is called constant polynomial.
- A polynomial of degree 1 is called linear polynomial.
- A polynomial of degree 2 is called quadratic polynomial.
- A polynomial of degree 3 is called cubic polynomial.
- A polynomial of degree 4 is called biquadratic polynomial.

## Zeroes Of A Polynomial

- Any real number `k’ is called a zero of a polynomial p(x), if p(K) = 0
- If `k’ is the zero of p(x), then we can also say `k’ is a root of the equation p(x) = 0

**Some Important Facts**

- Every linear polynomial in one variable has a unique zero.
- Every non-zero constant polynomial has no zero.
- Every real number is a zero of the zero polynomial

## Remainder Theorem

## Factor Theorem

## Algebraic Identities

- (x + y)
^{2}= x^{2}+ y^{2}+ 2xy - (x – y)
^{2}= x^{2}+ y^{2}– 2xy - x
^{2}– y^{2}= (x + y) (x – y) - (x + a) (x + b) = x2 + (a + b) x + ab
- (x + y + z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy + 2yz + 2zx - (x + y)
^{3}= x^{3}+ y^{3}+ 3xy (x + y) = x^{3}+ y^{3}+ 3x^{2}y + 3xy^{2} - (x – y)
^{3}= x^{3}– y^{3}– 3xy (x – y) = x^{3}– y^{3}– 3x^{2}y + 3xy^{2} - x
^{3}+ y^{3}= (x + y) (x^{2}+ y^{2}– xy) - x
^{3}– y^{3}= (x – y) (x^{2}+ y^{2}+ xy) - x
^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z) (x^{2}+ y^{2}+ z^{2}– xy – yz – zx)