Whakaoti i te -b^3+5b^2+24b

$$- b ^ { 3 } + 5 b ^ { 2 } + 24 b$$

Tauwehe

$$-b\left(b-8\right)\left(b+3\right)$$

Ngā Upane Otinga

Tauwehea te b.

$$b\left(-b^{2}+5b+24\right)$$

Whakaarohia te -b^{2}+5b+24. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -b^{2}+pb+qb+24. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=5 pq=-24=-24$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōrunga te p+q, 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 -24.

$$-1,24 -2,12 -3,8 -4,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$p=8 q=-3$$

Tuhia anō te -b^{2}+5b+24 hei \left(-b^{2}+8b\right)+\left(-3b+24\right).

$$\left(-b^{2}+8b\right)+\left(-3b+24\right)$$

Tauwehea te -b i te tuatahi me te -3 i te rōpū tuarua.

$$-b\left(b-8\right)-3\left(b-8\right)$$

Whakatauwehea atu te kīanga pātahi b-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(b-8\right)\left(-b-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$b\left(b-8\right)\left(-b-3\right)$$

Aromātai

$$-b\left(b-8\right)\left(b+3\right)$$