Whakaoti i te x^3-8x^2+12x

$${ x }^{ 3 } -8 { x }^{ 2 } +12x$$

Tauwehe

$$x\left(x-6\right)\left(x-2\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(x^{2}-8x+12\right)$$

Whakaarohia te x^{2}-8x+12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=1\times 12=12$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$-1,-12 -2,-6 -3,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -8.

$$a=-6 b=-2$$

Tuhia anō te x^{2}-8x+12 hei \left(x^{2}-6x\right)+\left(-2x+12\right).

$$\left(x^{2}-6x\right)+\left(-2x+12\right)$$

Tauwehea te x i te tuatahi me te -2 i te rōpū tuarua.

$$x\left(x-6\right)-2\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(x-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x\left(x-6\right)\left(x-2\right)$$

Aromātai

$$x\left(x-6\right)\left(x-2\right)$$