Whakaoti i te 12x^3-39x^2+30x

$$12 x ^ { 3 } - 39 x ^ { 2 } + 30 x$$

Tauwehe

$$3x\left(x-2\right)\left(4x-5\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(4x^{3}-13x^{2}+10x\right)$$

Whakaarohia te 4x^{3}-13x^{2}+10x. Tauwehea te x.

$$x\left(4x^{2}-13x+10\right)$$

Whakaarohia te 4x^{2}-13x+10. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 4x^{2}+ax+bx+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=4\times 10=40$$

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 40.

$$-1,-40 -2,-20 -4,-10 -5,-8$$

Tātaihia te tapeke mō ia takirua.

$$-1-40=-41 -2-20=-22 -4-10=-14 -5-8=-13$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-8 b=-5$$

Tuhia anō te 4x^{2}-13x+10 hei \left(4x^{2}-8x\right)+\left(-5x+10\right).

$$\left(4x^{2}-8x\right)+\left(-5x+10\right)$$

Tauwehea te 4x i te tuatahi me te -5 i te rōpū tuarua.

$$4x\left(x-2\right)-5\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(4x-5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3x\left(x-2\right)\left(4x-5\right)$$

Aromātai

$$3x\left(x-2\right)\left(4x-5\right)$$