Lutasin ang 5x^6-5x^4+x^3-x

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

I-factor

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

Mga Hakbang ng Solution

I-factor out ang x.

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

Isaalang-alang ang 5x^{5}-5x^{3}+x^{2}-1. Gawin ang grouping na 5x^{5}-5x^{3}+x^{2}-1=\left(5x^{5}-5x^{3}\right)+\left(x^{2}-1\right), at i-factor out ang 5x^{3} sa 5x^{5}-5x^{3}.

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

I-factor out ang common term na x^{2}-1 gamit ang distributive property.

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

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

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

I-rewrite ang kumpletong naka-factor na expression. Ang polynomial 5x^{3}+1 ay hindi naka-factor dahil wala itong anumang rational root.

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

I-evaluate

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