Lutasin ang x^4-x+x^3-1

$$x ^ { 4 } - x + x ^ { 3 } - 1$$

I-factor

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

Mga Hakbang ng Solution

Gawin ang grouping na x^{4}-x+x^{3}-1=\left(x^{4}-x\right)+\left(x^{3}-1\right), at i-factor out ang x sa x^{4}-x.

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

I-factor out ang common term na x^{3}-1 gamit ang distributive property.

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

Isaalang-alang ang x^{3}-1. I-rewrite ang x^{3}-1 bilang x^{3}-1^{3}. Maaaring i-factor ang difference ng mga cube gamit ang panuntunang: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

I-rewrite ang kumpletong naka-factor na expression. Ang polynomial x^{2}+x+1 ay hindi naka-factor dahil wala itong anumang rational root.

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

I-evaluate

$$x^{4}+x^{3}-x-1$$