Hello Students! 👋
Aaj hum Algebra ka ek bahut interesting chapter start karne wale hain — Polynomials. Ye word sunne mein thoda mushkil lag sakta hai, lekin trust me, ye bahut simple hai!
Polynomials basically maths ki language hai jisme hum numbers aur variables ko mix karke expressions banate hain.
🎥 Video Explanation
🇮🇳 Hindi Explanation
🇬🇧 English Explanation
📊 Infographic Summary
🤔 Polynomial Kya Hota Hai?
Imagine karo aap ek Lego train bana rahe ho. Train mein alag-alag dibbe (compartments) hote hain jo ek dusre se jude hote hain. Maths mein, har dibba ek Term hota hai, aur puri train ek Polynomial hoti hai. Jaise train ke dibbe connectors se jude hote hain, waise hi polynomial ke terms Plus (+) ya Minus (-) signs se jude hote hain.
Word Polynomial do words se milkar bana hai:
- Poly = Many (Bahut saare)
- Nomial = Terms (Hisse ya parts)
Toh, Polynomial ka matlab hai "Bahut saare terms wala expression".
✔ Example:
2x² + 5x - 3
Isme 3 terms hain: 2x², 5x, aur -3.
🧩 Components of a Polynomial
Ek polynomial 3 main cheezon se banta hai:
1. Variables (Chara)
Ye wo letters hote hain jinki value change ho sakti hai. Usually hum x, y, z use karte hain.
2. Coefficients (Gunank)
Variable ke saath jo number multiply hota hai, use Coefficient kehte hain.
In 5x, coefficient of x is 5.
In -7y², coefficient of y² is -7.
3. Constants (Achara)
Wo numbers jo akele hote hain aur jinki value change nahi hoti.
In 2x + 9, constant term is 9.
🛑 Rule: Kaunsa Expression Polynomial Hai?
Har algebraic expression polynomial nahi hota! Ek rule yaad rakhna:
📌 Important Rule:
Variable ki power (exponent) hamesha ek Whole
Number (0, 1, 2, 3...) honi chahiye.
✔ Polynomials (Valid):
x² + 2x(Powers: 2, 1 → Whole numbers)y³ - 1(Power: 3 → Whole number)5(Constant polynomial, x ki power 0 hai)
❌ Not Polynomials (Invalid):
x⁻¹ + 2(Power -1 whole number nahi hai)√x + 3(√x ka matlab x ki power 1/2, jo whole number nahi hai)1/x(Iska matlab x⁻¹, not allowed)
🔢 Special Types of Polynomials
1. Constant Polynomial
Sirf ek number, jisme koi variable nahi dikhta.
Example: 2, -5, 7
Actually, 2 ko hum 2x⁰ likh sakte hain (kyunki x⁰ = 1).
2. Zero Polynomial
Number 0 ko Zero Polynomial kaha jata hai.
📌 Aage Ka Content (Coming Next)
Ab humne basics samajh liye hain. Next lesson mein hum seekhenge:
- ✔ Polynomials in One Variable
- ✔ Degree of Polynomial
- ✔ Linear, Quadratic, and Cubic Polynomials