k^4+k^3+k+1= eching

$$k ^ { 4 } + k ^ { 3 } + k + 1 =$$

Omil

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

Yechim qadamlari

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

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

Distributiv funktsiyasidan foydalangan holda k+1 umumiy terminini chiqaring.

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

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

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

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

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

Baholash

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