P(x)=x^2+3x+2 eching

$$P ( x ) = x ^ { 2 } + 3 x + 2$$

Omil

$$\left(x+1\right)\left(x+2\right)$$

Yechim qadamlari

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

$$a+b=3 ab=1\times 2=2$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. Faqat bundan juftlik tizim yechimidir.

$$a=1 b=2$$

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

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

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

$$x\left(x+1\right)+2\left(x+1\right)$$

Distributiv funktsiyasidan foydalangan holda x+1 umumiy terminini chiqaring.

$$\left(x+1\right)\left(x+2\right)$$

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.

$$x^{2}+3x+2=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 2}}{2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-8}}{2}$$

9 ni -8 ga qo'shish.

$$x=\frac{-3±\sqrt{1}}{2}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±1}{2}$$

x=\frac{-3±1}{2} tenglamasini yeching, bunda ± musbat. -3 ni 1 ga qo'shish.

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

-2 ni 2 ga bo'lish.

$$x=-1$$

x=\frac{-3±1}{2} tenglamasini yeching, bunda ± manfiy. -3 dan 1 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 -1 ga va x_{2} uchun -2 ga bo‘ling.

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

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

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

Baholash

$$\left(x+1\right)\left(x+2\right)$$