f(x)=2a^3-a^2-7a+6 eching | Microsoft math hal qiluvchi

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Viktorina

Polynomial

5xshash muammolar:

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Klipbordga nusxa olish

\left(2a-3\right)\left(a^{2}+a-2\right)

Ratsional ildiz teoremasiga koʻra, koʻphadlarning barcha ratsional ildizlari \frac{p}{q} shakli ichida, bu yerda p konstant shart 6 bilan boʻlinadi va q yetakchi koeffisientni 2 boʻladi. Bunday bir ildiz – \frac{3}{2}. Uni 2a-3 bilan boʻlib, koʻphadni faktorlang.

p+q=1 pq=1\left(-2\right)=-2

Hisoblang: a^{2}+a-2. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda a^{2}+pa+qa-2 sifatida qayta yozilishi kerak. p va q ni topish uchun yechiladigan tizimni sozlang.

p=-1 q=2

pq manfiy boʻlganda, p va q da qarama-qarshi belgilar bor. p+q musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

\left(a^{2}-a\right)+\left(2a-2\right)

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

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

Birinchi guruhda a ni va ikkinchi guruhda 2 ni faktordan chiqaring.

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

Distributiv funktsiyasidan foydalangan holda a-1 umumiy terminini chiqaring.

\left(2a-3\right)\left(a-1\right)\left(a+2\right)

Toʻliq ajratilgan ifodani qaytadan yozing.