x^5-x^3+27x^2-27= eching

$$x ^ { 5 } - x ^ { 3 } + 27 x ^ { 2 } - 27 =$$

Omil

$$\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x^{2}-3x+9\right)$$

Yechim qadamlari

x^{5}-x^{3}+27x^{2}-27=\left(x^{5}-x^{3}\right)+\left(27x^{2}-27\right) misolini guruhlang hamda x^{3} ni birinchi va 27 ni ikkinchi guruhdan ajrating.

$$x^{3}\left(x^{2}-1\right)+27\left(x^{2}-1\right)$$

Distributiv funktsiyasidan foydalangan holda x^{2}-1 umumiy terminini chiqaring.

$$\left(x^{2}-1\right)\left(x^{3}+27\right)$$

Hisoblang: x^{2}-1. x^{2}-1 ni x^{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).

$$\left(x-1\right)\left(x+1\right)$$

Hisoblang: x^{3}+27. x^{3}+27 ni x^{3}+3^{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).

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

Toʻliq ajratilgan ifodani qaytadan yozing. Koʻphadli x^{2}-3x+9 faktorlanmagan, chunki unda ratsional ildizlar topilmadi.

$$\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x^{2}-3x+9\right)$$

Baholash

$$x^{5}-x^{3}+27x^{2}-27$$