Q(x)=-x^3+3x-2 eching | Microsoft math hal qiluvchi

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https://www.quora.com/Given-the-function-f-x-x-3+3x-1-how-do-you-find-where-the-slope-of-the-line-is-positive-and-negative-where-the-graph-is-rising-and-falling

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\left(x+2\right)\left(-x^{2}+2x-1\right)

Ratsional ildiz teoremasiga koʻra, koʻphadlarning barcha ratsional ildizlari \frac{p}{q} shakli ichida, bu yerda p konstant shart -2 bilan boʻlinadi va q yetakchi koeffisientni -1 boʻladi. Bunday bir ildiz – -2. Uni x+2 bilan boʻlib, koʻphadni faktorlang.

a+b=2 ab=-\left(-1\right)=1

Hisoblang: -x^{2}+2x-1. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx-1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

a=1 b=1

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. Faqat bundan juftlik tizim yechimidir.

\left(-x^{2}+x\right)+\left(x-1\right)

-x^{2}+2x-1 ni \left(-x^{2}+x\right)+\left(x-1\right) sifatida qaytadan yozish.

-x\left(x-1\right)+x-1

-x^{2}+x ichida -x ni ajrating.

\left(x-1\right)\left(-x+1\right)

Distributiv funktsiyasidan foydalangan holda x-1 umumiy terminini chiqaring.

\left(x-1\right)\left(-x+1\right)\left(x+2\right)

Toʻliq ajratilgan ifodani qaytadan yozing.