Whakaoti i te 4x^3+4x^2-48x

$$4 x ^ { 3 } + 4 x ^ { 2 } - 48 x$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(x^{3}+x^{2}-12x\right)$$

Whakaarohia te x^{3}+x^{2}-12x. Tauwehea te x.

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

Whakaarohia te x^{2}+x-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.

$$a+b=1 ab=1\left(-12\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. 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.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-3 b=4$$

Tuhia anō te x^{2}+x-12 hei \left(x^{2}-3x\right)+\left(4x-12\right).

$$\left(x^{2}-3x\right)+\left(4x-12\right)$$

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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