-3x^2-12x+36= eching

$$- 3 x ^ { 2 } - 12 x + 36 =$$

Omil

$$3\left(2-x\right)\left(x+6\right)$$

Yechim qadamlari

3 omili.

$$3\left(-x^{2}-4x+12\right)$$

Hisoblang: -x^{2}-4x+12. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+12 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-4 ab=-12=-12$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -12-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-12 2,-6 3,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$1-12=-11 2-6=-4 3-4=-1$$

Yechim – -4 yigʻindisini beruvchi juftlik.

$$a=2 b=-6$$

-x^{2}-4x+12 ni \left(-x^{2}+2x\right)+\left(-6x+12\right) sifatida qaytadan yozish.

$$\left(-x^{2}+2x\right)+\left(-6x+12\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 6 ni faktordan chiqaring.

$$x\left(-x+2\right)+6\left(-x+2\right)$$

Distributiv funktsiyasidan foydalangan holda -x+2 umumiy terminini chiqaring.

$$\left(-x+2\right)\left(x+6\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3\left(-x+2\right)\left(x+6\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$-3x^{2}-12x+36=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-3\right)\times 36}}{2\left(-3\right)}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-3\right)\times 36}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+12\times 36}}{2\left(-3\right)}$$

12 ni 36 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+432}}{2\left(-3\right)}$$

144 ni 432 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{576}}{2\left(-3\right)}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±24}{2\left(-3\right)}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±24}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{12±24}{-6}$$

x=\frac{12±24}{-6} tenglamasini yeching, bunda ± musbat. 12 ni 24 ga qo'shish.

$$x=\frac{36}{-6}$$

36 ni -6 ga bo'lish.

$$x=-6$$

x=\frac{12±24}{-6} tenglamasini yeching, bunda ± manfiy. 12 dan 24 ni ayirish.

$$x=-\frac{12}{-6}$$

-12 ni -6 ga bo'lish.

$$x=2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -6 ga va x_{2} uchun 2 ga bo‘ling.

$$-3x^{2}-12x+36=-3\left(x-\left(-6\right)\right)\left(x-2\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$-3x^{2}-12x+36=-3\left(x+6\right)\left(x-2\right)$$

Baholash

$$3\left(2-x\right)\left(x+6\right)$$