1. Synthetic division ek tarah ka shortcut method hai jo hum polynomial division ke liye use karte hain, khas taur par jab divisor linear form mein ho, jaise $x - c$. 2. Iska maksad hai polynomial ko divide karna bina lambi division ke process ke, jisse calculation jaldi aur asaan ho jata hai. 3. Formula ya rule: Agar aapke paas polynomial $P(x)$ hai aur aap usse divide karna chahte hain $x - c$ se, to synthetic division mein aap sirf coefficients ke saath kaam karte hain. 4. Steps: - Sabse pehle polynomial ke coefficients likho. - Phir divisor ke root $c$ ko likho. - Pehla coefficient neeche likh do. - Uske baad, neeche wale number ko $c$ se multiply karo aur agle coefficient ke saath add karo. - Yeh process tab tak repeat karo jab tak saare coefficients process na ho jayein. 5. Jo numbers neeche likhe hain, woh quotient ke coefficients hain, aur last number remainder hota hai. 6. Example: Divide $2x^3 + 3x^2 - 5x + 6$ by $x - 2$. - Coefficients: 2, 3, -5, 6 - $c = 2$ - Neeche likho 2 - Multiply 2*2=4, add 3+4=7 - Multiply 7*2=14, add -5+14=9 - Multiply 9*2=18, add 6+18=24 - Quotient coefficients: 2, 7, 9; remainder: 24 7. Iska matlab quotient hai $2x^2 + 7x + 9$ aur remainder 24. Yeh method polynomial division ko bahut asaan aur tezi se solve karne mein madad karta hai.