-3x^2-6x+9 eching

$$- 3 x ^ { 2 } - 6 x + 9$$

Omil

$$3\left(1-x\right)\left(x+3\right)$$

Yechim qadamlari

3 omili.

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

Hisoblang: -x^{2}-2x+3. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+3 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=-3=-3$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=1 b=-3$$

-x^{2}-2x+3 ni \left(-x^{2}+x\right)+\left(-3x+3\right) sifatida qaytadan yozish.

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

Birinchi guruhda x ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$x\left(-x+1\right)+3\left(-x+1\right)$$

Distributiv funktsiyasidan foydalangan holda -x+1 umumiy terminini chiqaring.

$$\left(-x+1\right)\left(x+3\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3\left(-x+1\right)\left(x+3\right)$$

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.

$$-3x^{2}-6x+9=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-3\right)\times 9}}{2\left(-3\right)}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-3\right)\times 9}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+12\times 9}}{2\left(-3\right)}$$

12 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+108}}{2\left(-3\right)}$$

36 ni 108 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{144}}{2\left(-3\right)}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±12}{2\left(-3\right)}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±12}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{6±12}{-6}$$

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

$$x=\frac{18}{-6}$$

18 ni -6 ga bo'lish.

$$x=-3$$

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

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

-6 ni -6 ga bo'lish.

$$x=1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -3 ga va x_{2} uchun 1 ga bo‘ling.

$$-3x^{2}-6x+9=-3\left(x-\left(-3\right)\right)\left(x-1\right)$$

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

$$-3x^{2}-6x+9=-3\left(x+3\right)\left(x-1\right)$$

Baholash

$$3\left(1-x\right)\left(x+3\right)$$