Introduction to Polynomials | Class 10 Mathematics

01 · THE BASICS

What is a Polynomial?

An algebraic expression of the form p(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀ (where exponents of variable x are non-negative integers) is called a polynomial in x.

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Degree of a Polynomial

The highest power of the variable x in a polynomial p(x) is called the degree of the polynomial.

02 · TYPES OF POLYNOMIALS

Types of Polynomials by Degree

Deg 1

Linear Polynomial

Form: ax + b (where a ≠ 0). Example: 2x - 3

Deg 2

Quadratic Polynomial

Form: ax² + bx + c (where a ≠ 0). Example: x² - 3x - 4

Deg 3

Cubic Polynomial

Form: ax³ + bx² + cx + d (where a ≠ 0). Example: x³ - 2x²

03 · ZEROES OF A POLYNOMIAL

What is a Zero of a Polynomial?

A real number k is said to be a zero of a polynomial p(x) if:

p(k) = 0

EXAMPLE 1

Find the zero of p(x) = 2x + 3

Set p(x) = 0:

2x + 3 = 0
2x = -3 ⟹ x = -3/2

Hence, -3/2 is the zero of the linear polynomial p(x) = 2x + 3.

04 · QUICK SUMMARY

Key Takeaways

Powers of variable in a polynomial must be non-negative integers (0, 1, 2, 3...).

Linear polynomial has degree 1, Quadratic has degree 2, Cubic has degree 3.

If p(k) = 0, then k is called a zero of polynomial p(x).