🔍 What is a Polynomial?
A polynomial is an algebraic expression that includes variables, constants, and exponents combined using mathematical operations.
✅ Example:
This is a quadratic polynomial (degree 2).
🔹 Types of Polynomials
Type | Example | Degree |
---|---|---|
Constant | 5 | 0 |
Linear | 1 | |
Quadratic | 2 | |
Cubic | 3 |
🎯 Zeroes of a Polynomial
The zeroes (or roots) of a polynomial are the values of that make the polynomial equal to zero.
✅ Example:
If ,
Then the zeroes are:
Because and
🔁 Relationship Between Zeroes and Coefficients
For a quadratic polynomial , if α and β are the zeroes:
-
Sum of zeroes =
-
Product of zeroes =
✅ Example:
For ,
Sum = 5, Product = 6 → Roots: 2 and 3
🧮 Division Algorithm for Polynomials
If and are two polynomials, then:
Where:
-
= Dividend
-
= Divisor
-
= Quotient
-
= Remainder
-
Degree of < Degree of
✅ Quick Revision
-
A polynomial is an expression like
-
Degree = highest power of variable
-
Use factorization and division algorithm for solving
-
Know the relation between zeroes and coefficients
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