📘 Chapter 2 – Polynomials (Ultra-Easy)
🔹 1. What is a Polynomial?
Very Simple Meaning
A polynomial is a maths expression made by:
- numbers
- letters (x, y)
- powers of letters (like x², x³)
👉 Only whole number powers are allowed
👉 No division by variable
বহুপদী মানে:
সংখ্যা + চলক + চলকৰ ঘাত থকা এটা অভিব্যক্তি
য’ত ঘাত 0, 1, 2, 3… হয়।
✔ Examples
2x + 3
x² − 5x + 7
7
❌ Not Polynomial
1/x (x⁻¹)
√x (x¹ᐟ²)
🔹 2. Parts of a Polynomial
(a) Term (পদ)
Each part separated by + or −
Example:
3x² − 2x + 1
Terms: 3x², −2x, 1
(b) Coefficient (গুণক)
Number in front of variable
Example:
In 5x → coefficient = 5
In −3x² → coefficient = −3
(c) Constant Term
Term without variable
Example:
x² + 4x + 9
🔹 3. Degree of a Polynomial
Rule (Very Important)
👉 Degree = Highest power of variable
| Polynomial | Degree |
|---|---|
| 5 | 0 |
| 3x | 1 |
| x² + 2x | 2 |
| 4x³ − x | 3 |
🔹 4. Types of Polynomials (By Terms)
| Terms | Name | Example |
|---|---|---|
| 1 | Monomial | 5x |
| 2 | Binomial | x + 3 |
| 3 | Trinomial | x² + 2x + 1 |
🔹 5. Types of Polynomials (By Degree)
| Degree | Name | Example |
|---|---|---|
| 0 | Constant | 7 |
| 1 | Linear | 2x + 1 |
| 2 | Quadratic | x² + 3x |
| 3 | Cubic | x³ − x |
🔹 6. Value of a Polynomial
Easy Rule
👉 Put value of x and solve
Example:
Find value of 2x + 3 when x = 4
= 2(4) + 3
= 11
🔹 7. Zero of a Polynomial
Meaning (Super Easy)
If polynomial becomes 0 at some value of x,
that x value is called zero.
য’ত বহুপদীৰ মান শূন্য হয় → সেই x মানেই zero
Example
x − 5 = 0
x = 5 → zero
🔹 8. How to Find Zero?
Step-by-Step
- Write polynomial
- Make it equal to 0
- Solve like equation
Example:
2x + 6 = 0
2x = −6
x = −3 → zero
🔹 9. Zero Using Graph
Very Easy Idea
- Graph cuts x-axis
- That point = zero
x-axis কাটে যিমানবাৰ → zero সিমানটা
🔹 10. Number of Zeros
| Polynomial | Zeros |
|---|---|
| Linear | 1 |
| Quadratic | Max 2 |
| Cubic | Max 3 |
🔹 11. Important Exam Facts ⭐
✔ Polynomial never has √x or 1/x
✔ Constant degree = 0
✔ Linear graph = straight line
✔ Zero means f(x) = 0
🔹 12. Common Mistakes ❌
❌ Writing √x as polynomial
❌ Wrong degree
❌ Forgetting sign + or −
❌ Counting y-axis instead of x-axis
🔁 One-Line Quick Revision
- Polynomial → no negative power
- Degree → highest power
- Zero → value where result is 0
- Graph → x-axis cut