Whakaoti i te 18x^4-42x^3+24x^2?

$$18 x ^ { 4 } - 42 x ^ { 3 } + 24 x ^ { 2 } ?$$

Tauwehe

$$6\left(x-1\right)\left(3x-4\right)x^{2}$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(3x^{4}-7x^{3}+4x^{2}\right)$$

Whakaarohia te 3x^{4}-7x^{3}+4x^{2}. Tauwehea te x^{2}.

$$x^{2}\left(3x^{2}-7x+4\right)$$

Whakaarohia te 3x^{2}-7x+4. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=3\times 4=12$$

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 -7.

$$a=-4 b=-3$$

Tuhia anō te 3x^{2}-7x+4 hei \left(3x^{2}-4x\right)+\left(-3x+4\right).

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

Tauwehea te x i te tuatahi me te -1 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi 3x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x-4\right)\left(x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6x^{2}\left(3x-4\right)\left(x-1\right)$$

Aromātai

$$6\left(x-1\right)\left(3x-4\right)x^{2}$$