01 · DEFINITION & DEGREE
What is a Polynomial?
An algebraic expression of the form p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀, where non-negative integers n represent exponent powers, is called a polynomial in variable x.
CLASSIFICATION BY DEGREE
Degree of Polynomial
• Constant Polynomial (Degree 0): p(x) = 5 (Non-zero constant polynomial degree is 0).
• Linear Polynomial (Degree 1): p(x) = 2x + 3
• Quadratic Polynomial (Degree 2): p(x) = x² - 4x + 4
• Cubic Polynomial (Degree 3): p(x) = x³ - 3x² + 3x - 1
02 · ZEROES OF A POLYNOMIAL
Finding Value & Zeroes p(x) = 0
A real number c is called a zero of a polynomial p(x) if p(c) = 0.
SOLVED EXAMPLE
Find the zero of the polynomial p(x) = 2x + 5
Set p(x) = 0:
2x + 5 = 0
2x = -5 ⟹ x = -5/2
2x = -5 ⟹ x = -5/2
Hence, -5/2 is the zero of the linear polynomial p(x).