Whakaoti i te 5x^6-5x^4+x^3-x

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

Tauwehe

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

Ngā Upane Otinga

Tauwehea te x.

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

Whakaarohia te 5x^{5}-5x^{3}+x^{2}-1. Mahia te whakarōpūtanga 5x^{5}-5x^{3}+x^{2}-1=\left(5x^{5}-5x^{3}\right)+\left(x^{2}-1\right), ka whakatauwehea atu 5x^{3} i te 5x^{5}-5x^{3}.

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

Whakatauwehea atu te kīanga pātahi x^{2}-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Whakaarohia te x^{2}-1. Tuhia anō te x^{2}-1 hei x^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Me tuhi anō te kīanga whakatauwehe katoa. Kāore te pūrau 5x^{3}+1 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

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

Aromātai

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