x^9-x^6-x^3+1 eching

$$x ^ { 9 } - x ^ { 6 } - x ^ { 3 } + 1$$

Omil

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

Yechim qadamlari

x^{9}-x^{6}-x^{3}+1=\left(x^{9}-x^{6}\right)+\left(-x^{3}+1\right) misolini guruhlang hamda x^{6} ni birinchi va -1 ni ikkinchi guruhdan ajrating.

$$x^{6}\left(x^{3}-1\right)-\left(x^{3}-1\right)$$

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

$$\left(x^{3}-1\right)\left(x^{6}-1\right)$$

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).

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

Hisoblang: x^{6}-1. x^{6}-1 ni \left(x^{3}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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).

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

Hisoblang: x^{3}+1. x^{3}+1 ni x^{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).

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

Toʻliq ajratilgan ifodani qaytadan yozing. Quyidagi koʻphadlar faktorlanmagan, ularda hech qanday ratsional ildizlar topilmadi: x^{2}-x+1,x^{2}+x+1.

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

Baholash

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