p(x)=2x^3+24x^2-56x eching | Microsoft math hal qiluvchi

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Baham ko'rish

Klipbordga nusxa olish

2\left(x^{3}+12x^{2}-28x\right)

2 omili.

x\left(x^{2}+12x-28\right)

Hisoblang: x^{3}+12x^{2}-28x. x omili.

a+b=12 ab=1\left(-28\right)=-28

Hisoblang: x^{2}+12x-28. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-28 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

-1,28 -2,14 -4,7

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -28-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

-1+28=27 -2+14=12 -4+7=3

Har bir juftlik yigʻindisini hisoblang.

a=-2 b=14

Yechim – 12 yigʻindisini beruvchi juftlik.

\left(x^{2}-2x\right)+\left(14x-28\right)

x^{2}+12x-28 ni \left(x^{2}-2x\right)+\left(14x-28\right) sifatida qaytadan yozish.

x\left(x-2\right)+14\left(x-2\right)

Birinchi guruhda x ni va ikkinchi guruhda 14 ni faktordan chiqaring.

\left(x-2\right)\left(x+14\right)

Distributiv funktsiyasidan foydalangan holda x-2 umumiy terminini chiqaring.

2x\left(x-2\right)\left(x+14\right)

Toʻliq ajratilgan ifodani qaytadan yozing.