3s^2+16s+5 eching

$$3 s ^ { 2 } + 16 s + 5$$

Omil

$$\left(s+5\right)\left(3s+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 3s^{2}+as+bs+5 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=16 ab=3\times 5=15$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 15-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,15 3,5$$

Har bir juftlik yigʻindisini hisoblang.

$$1+15=16 3+5=8$$

Yechim – 16 yigʻindisini beruvchi juftlik.

$$a=1 b=15$$

3s^{2}+16s+5 ni \left(3s^{2}+s\right)+\left(15s+5\right) sifatida qaytadan yozish.

$$\left(3s^{2}+s\right)+\left(15s+5\right)$$

Birinchi guruhda s ni va ikkinchi guruhda 5 ni faktordan chiqaring.

$$s\left(3s+1\right)+5\left(3s+1\right)$$

Distributiv funktsiyasidan foydalangan holda 3s+1 umumiy terminini chiqaring.

$$\left(3s+1\right)\left(s+5\right)$$

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.

$$3s^{2}+16s+5=0$$

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.

$$s=\frac{-16±\sqrt{16^{2}-4\times 3\times 5}}{2\times 3}$$

16 kvadratini chiqarish.

$$s=\frac{-16±\sqrt{256-4\times 3\times 5}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$s=\frac{-16±\sqrt{256-12\times 5}}{2\times 3}$$

-12 ni 5 marotabaga ko'paytirish.

$$s=\frac{-16±\sqrt{256-60}}{2\times 3}$$

256 ni -60 ga qo'shish.

$$s=\frac{-16±\sqrt{196}}{2\times 3}$$

196 ning kvadrat ildizini chiqarish.

$$s=\frac{-16±14}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$s=\frac{-16±14}{6}$$

s=\frac{-16±14}{6} tenglamasini yeching, bunda ± musbat. -16 ni 14 ga qo'shish.

$$s=-\frac{2}{6}$$

\frac{-2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=-\frac{1}{3}$$

s=\frac{-16±14}{6} tenglamasini yeching, bunda ± manfiy. -16 dan 14 ni ayirish.

$$s=-\frac{30}{6}$$

-30 ni 6 ga bo'lish.

$$s=-5$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{1}{3} ga va x_{2} uchun -5 ga bo‘ling.

$$3s^{2}+16s+5=3\left(s-\left(-\frac{1}{3}\right)\right)\left(s-\left(-5\right)\right)$$

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

$$3s^{2}+16s+5=3\left(s+\frac{1}{3}\right)\left(s+5\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{3} ni s ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$3s^{2}+16s+5=3\times \frac{3s+1}{3}\left(s+5\right)$$

3 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$3s^{2}+16s+5=\left(3s+1\right)\left(s+5\right)$$

Baholash

$$\left(s+5\right)\left(3s+1\right)$$