Whakaoti i te x^2-6x+5x-30

$$x ^ { 2 } - 6 x + 5 x - 30$$

Tauwehe

$$\left(x-6\right)\left(x+5\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$x^{2}-x-30$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=1\left(-30\right)=-30$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -30.

$$1,-30 2,-15 3,-10 5,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

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

$$a=-6 b=5$$

Tuhia anō te x^{2}-x-30 hei \left(x^{2}-6x\right)+\left(5x-30\right).

$$\left(x^{2}-6x\right)+\left(5x-30\right)$$

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

$$x\left(x-6\right)+5\left(x-6\right)$$

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

$$\left(x-6\right)\left(x+5\right)$$

Aromātai

$$\left(x-6\right)\left(x+5\right)$$

Ngā Upane Otinga

Pahekotia te -6x me 5x, ka -x.

$$x^{2}-x-30$$