f(x)=x^4+3x^3+x^2/3+x eching

$$f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + \frac { x ^ { 2 } } { 3 } + x$$

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{4}+3x^{3}+x ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{3\left(x^{4}+3x^{3}+x\right)}{3}+\frac{x^{2}}{3}$$

\frac{3\left(x^{4}+3x^{3}+x\right)}{3} va \frac{x^{2}}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3\left(x^{4}+3x^{3}+x\right)+x^{2}}{3}$$

3\left(x^{4}+3x^{3}+x\right)+x^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x^{4}+9x^{3}+3x+x^{2}}{3}$$

Omil

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

Yechim qadamlari

\frac{1}{3} omili.

$$\frac{3x^{4}+9x^{3}+x^{2}+3x}{3}$$

Hisoblang: 3x^{4}+9x^{3}+x^{2}+3x. x omili.

$$x\left(3x^{3}+9x^{2}+x+3\right)$$

Hisoblang: 3x^{3}+9x^{2}+x+3. 3x^{3}+9x^{2}+x+3=\left(3x^{3}+9x^{2}\right)+\left(x+3\right) misolini guruhlang hamda 3x^{3}+9x^{2} ichidagi 3x^{2} ni ajrating.

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

Distributiv funktsiyasidan foydalangan holda x+3 umumiy terminini chiqaring.

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

Toʻliq ajratilgan ifodani qaytadan yozing. Koʻphadli 3x^{2}+1 faktorlanmagan, chunki unda ratsional ildizlar topilmadi.

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