-x^4-4x^3+16x^2+64x eching

$$- x ^ { 4 } - 4 x ^ { 3 } + 16 x ^ { 2 } + 64 x$$

Omil

$$-x\left(x-4\right)\left(x+4\right)^{2}$$

Yechim qadamlari

x omili.

$$x\left(-x^{3}-4x^{2}+16x+64\right)$$

Hisoblang: -x^{3}-4x^{2}+16x+64. -x^{3}-4x^{2}+16x+64=\left(-x^{3}-4x^{2}\right)+\left(16x+64\right) misolini guruhlang hamda x^{2} ni birinchi va -16 ni ikkinchi guruhdan ajrating.

$$x^{2}\left(-x-4\right)-16\left(-x-4\right)$$

Distributiv funktsiyasidan foydalangan holda -x-4 umumiy terminini chiqaring.

$$\left(-x-4\right)\left(x^{2}-16\right)$$

Hisoblang: x^{2}-16. x^{2}-16 ni x^{2}-4^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$x\left(-x-4\right)\left(x-4\right)\left(x+4\right)$$

Baholash

$$-x\left(x-4\right)\left(x+4\right)^{2}$$