x^4+3x^3-x-3.x^3+x^2-5x+3 eching

$$x ^ { 4 } + 3 x ^ { 3 } - x - 3 . x ^ { 3 } + x ^ { 2 } - 5 x + 3$$

Omil

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

Yechim qadamlari

x^{4}+3x^{3}-x-3=\left(x^{4}+3x^{3}\right)+\left(-x-3\right) misolini guruhlang hamda x^{3} ni birinchi va -1 ni ikkinchi guruhdan ajrating.

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

Distributiv funktsiyasidan foydalangan holda x+3 umumiy terminini chiqaring.

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

Hisoblang: x^{3}-1. x^{3}-1 ni x^{3}-1^{3} sifatida qaytadan yozish. Kublarning farqini ushbu formula bilan hisoblash mumkin: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

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

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

Baholash

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