8x^2+43x+44 eching

$$8 x ^ { 2 } + 43 x + 44$$

Omil

$$\left(x+4\right)\left(8x+11\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 8x^{2}+ax+bx+44 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=43 ab=8\times 44=352$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 352-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,352 2,176 4,88 8,44 11,32 16,22$$

Har bir juftlik yigʻindisini hisoblang.

$$1+352=353 2+176=178 4+88=92 8+44=52 11+32=43 16+22=38$$

Yechim – 43 yigʻindisini beruvchi juftlik.

$$a=11 b=32$$

8x^{2}+43x+44 ni \left(8x^{2}+11x\right)+\left(32x+44\right) sifatida qaytadan yozish.

$$\left(8x^{2}+11x\right)+\left(32x+44\right)$$

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

$$x\left(8x+11\right)+4\left(8x+11\right)$$

Distributiv funktsiyasidan foydalangan holda 8x+11 umumiy terminini chiqaring.

$$\left(8x+11\right)\left(x+4\right)$$

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.

$$8x^{2}+43x+44=0$$

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.

$$x=\frac{-43±\sqrt{43^{2}-4\times 8\times 44}}{2\times 8}$$

43 kvadratini chiqarish.

$$x=\frac{-43±\sqrt{1849-4\times 8\times 44}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-43±\sqrt{1849-32\times 44}}{2\times 8}$$

-32 ni 44 marotabaga ko'paytirish.

$$x=\frac{-43±\sqrt{1849-1408}}{2\times 8}$$

1849 ni -1408 ga qo'shish.

$$x=\frac{-43±\sqrt{441}}{2\times 8}$$

441 ning kvadrat ildizini chiqarish.

$$x=\frac{-43±21}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-43±21}{16}$$

x=\frac{-43±21}{16} tenglamasini yeching, bunda ± musbat. -43 ni 21 ga qo'shish.

$$x=-\frac{22}{16}$$

\frac{-22}{16} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{11}{8}$$

x=\frac{-43±21}{16} tenglamasini yeching, bunda ± manfiy. -43 dan 21 ni ayirish.

$$x=-\frac{64}{16}$$

-64 ni 16 ga bo'lish.

$$x=-4$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{11}{8} ga va x_{2} uchun -4 ga bo‘ling.

$$8x^{2}+43x+44=8\left(x-\left(-\frac{11}{8}\right)\right)\left(x-\left(-4\right)\right)$$

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

$$8x^{2}+43x+44=8\left(x+\frac{11}{8}\right)\left(x+4\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{11}{8} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$8x^{2}+43x+44=8\times \frac{8x+11}{8}\left(x+4\right)$$

8 va 8 ichida eng katta umumiy 8 faktorini bekor qiling.

$$8x^{2}+43x+44=\left(8x+11\right)\left(x+4\right)$$

Baholash

$$\left(x+4\right)\left(8x+11\right)$$