1.4-bo'lim : Polinomlar
1-18 muammolar uchun ko'rsatilgan operatsiyani bajaring va natija darajasini aniqlang.
- \(10{x^5} + 2{x^3} - 1\)-ni \(8{x^4} - {x^3} + 16{x^2}\)-ga qo'shing
- \(7{t^2} - 13t + 4\)-ni \( - 6{t^2} + 13t - 4\)-ga qo'shing
- \({z^3} + 2{z^2} - 15z + 7\) dan \( - 12{z^2} + 9z - 3\) ni ayiring
- \(150{x^3} + 8x - 14\) dan \(100{x^4} - 19{x^2} - 7x\) ni ayiring
- \({w^5}\) dan \({w^4} + {w^3} + {w^2} + w + 1\) ni ayiring
- \(6{y^2}\left( {3 - {y^2} + 2{y^3}} \right)\)
- \({x^9}\left( {{x^2} + 7x - 4} \right)\)
- \(\left( {7x - 5} \right)\left( {4 - 10x} \right)\)
- \(\left( {4 + 9{t^2}} \right)\left( {{t^3} - 3t} \right)\)
- \(\left( {1 + 8y} \right)\left( {{y^3} - 4{y^2} + 7} \right)\)
- \(7\left( {x - 9} \right)\left( {2x + 3} \right)\)
- \({z^2}\left( {1 - {z^2}} \right)\left( {1 + {z^2}} \right)\)
- \(\left( {2 - x + 4{x^2}} \right)\left( {6x + 7} \right)\)
- \(\left( {10{w^2} - 4w + 9} \right)\left( {{w^3} + 5{w^2} + 2} \right)\)
- \(10{\left( {x + 3{x^2}} \right)^2}\)
- \(\left( {1 - 5y} \right){\left( {4 + y} \right)^2}\)
- \({x^2} - 7x + 10\) dan \(\left( {3 - x} \right)\left( {3 + x} \right)\) ni ayiring
- \({\left( {x + 9{x^3}} \right)^2}\) dan \({\left( {4{x^2} - 1} \right)^2}\) ni ayiring
- Agar n darajali ko‘phadni va m darajali ko‘phadni ko‘paytirsak, natija qanday daraja bo‘ladi?
- Agar \(n < m\) bilan n va m darajali 2 ta ko‘phadni qo‘shsak, natijaning darajasi qanday bo‘ladi?
- Agar \(n < m\) bilan n va m darajali 2 ta ko‘phadni ayirsak, natija qanday darajaga teng bo‘ladi?
- Agar biz \(n\) darajali ikkita ko'phadni qo'shsak, natijada \(n\) darajasi bo'lmasligi mumkinmi? Agar iloji bo'lsa, yig'indisi \(n\) darajasiga ega bo'lmagan \(n\) darajali ikkita ko'phadga misol keltira olasizmi?
- Agar ikkalasi ham \(n\) darajali ikkita ko'phadni ayirsak, natijada \(n\) darajasi bo'lmasligi mumkinmi? Iloji bo'lsa, ikkalasi ham \(n\) darajasidagi ikkita ko'phadga misol keltira olasizmi, ularning farqi \(n\) darajasiga ega emasmi?