5x^6-5x^4+x^3-x eching

$$5 { x }^{ 6 } -5 { x }^{ 4 } + { x }^{ 3 } -x$$

Omil

$$x\left(x-1\right)\left(x+1\right)\left(5x^{3}+1\right)$$

Yechim qadamlari

x omili.

$$x\left(5x^{5}-5x^{3}+x^{2}-1\right)$$

Hisoblang: 5x^{5}-5x^{3}+x^{2}-1. 5x^{5}-5x^{3}+x^{2}-1=\left(5x^{5}-5x^{3}\right)+\left(x^{2}-1\right) misolini guruhlang hamda 5x^{5}-5x^{3} ichidagi 5x^{3} ni ajrating.

$$5x^{3}\left(x^{2}-1\right)+x^{2}-1$$

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

$$\left(x^{2}-1\right)\left(5x^{3}+1\right)$$

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).

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

Toʻliq ajratilgan ifodani qaytadan yozing. Koʻphadli 5x^{3}+1 faktorlanmagan, chunki unda ratsional ildizlar topilmadi.

$$x\left(x-1\right)\left(x+1\right)\left(5x^{3}+1\right)$$

Baholash

$$x\left(x^{2}-1\right)\left(5x^{3}+1\right)$$