-x^2-2x+8 eching

$$- x ^ { 2 } - 2 x + 8$$

Omil

$$\left(2-x\right)\left(x+4\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+8 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=-8=-8$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -8-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-8 2,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$1-8=-7 2-4=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=2 b=-4$$

-x^{2}-2x+8 ni \left(-x^{2}+2x\right)+\left(-4x+8\right) sifatida qaytadan yozish.

$$\left(-x^{2}+2x\right)+\left(-4x+8\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 4 ni faktordan chiqaring.

$$x\left(-x+2\right)+4\left(-x+2\right)$$

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

$$\left(-x+2\right)\left(x+4\right)$$

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.

$$-x^{2}-2x+8=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 8}}{2\left(-1\right)}$$

4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+32}}{2\left(-1\right)}$$

4 ni 32 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{36}}{2\left(-1\right)}$$

36 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±6}{2\left(-1\right)}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±6}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±6}{-2}$$

x=\frac{2±6}{-2} tenglamasini yeching, bunda ± musbat. 2 ni 6 ga qo'shish.

$$x=\frac{8}{-2}$$

8 ni -2 ga bo'lish.

$$x=-4$$

x=\frac{2±6}{-2} tenglamasini yeching, bunda ± manfiy. 2 dan 6 ni ayirish.

$$x=-\frac{4}{-2}$$

-4 ni -2 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 -4 ga va x_{2} uchun 2 ga bo‘ling.

$$-x^{2}-2x+8=-\left(x-\left(-4\right)\right)\left(x-2\right)$$

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

$$-x^{2}-2x+8=-\left(x+4\right)\left(x-2\right)$$

Baholash

$$\left(2-x\right)\left(x+4\right)$$