f(x)=1/4x^4-x^3-x^2+4x eching

$$f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - x ^ { 3 } - x ^ { 2 } + 4 x$$

Omil

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

Yechim qadamlari

\frac{1}{4} omili.

$$\frac{x^{4}-4x^{3}-4x^{2}+16x}{4}$$

Hisoblang: x^{4}-4x^{3}-4x^{2}+16x. x omili.

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

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

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

Distributiv funktsiyasidan foydalangan holda x-4 umumiy terminini chiqaring.

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

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

$$\left(x-2\right)\left(x+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

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

Baholash

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