x^4-x+x^3-1 eching

$$x ^ { 4 } - x + x ^ { 3 } - 1$$

Omil

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

Yechim qadamlari

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

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

Distributiv funktsiyasidan foydalangan holda x^{3}-1 umumiy terminini chiqaring.

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

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.

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

Baholash

$$x^{4}+x^{3}-x-1$$