Whakaoti i te 6y^3-53y^2-9y

$$6 y ^ { 3 } - 53 y ^ { 2 } - 9 y$$

Tauwehe

$$y\left(y-9\right)\left(6y+1\right)$$

Ngā Upane Otinga

Tauwehea te y.

$$y\left(6y^{2}-53y-9\right)$$

Whakaarohia te 6y^{2}-53y-9. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6y^{2}+ay+by-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-53 ab=6\left(-9\right)=-54$$

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 -54.

$$1,-54 2,-27 3,-18 6,-9$$

Tātaihia te tapeke mō ia takirua.

$$1-54=-53 2-27=-25 3-18=-15 6-9=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -53.

$$a=-54 b=1$$

Tuhia anō te 6y^{2}-53y-9 hei \left(6y^{2}-54y\right)+\left(y-9\right).

$$\left(6y^{2}-54y\right)+\left(y-9\right)$$

Whakatauwehea atu 6y i te 6y^{2}-54y.

$$6y\left(y-9\right)+y-9$$

Whakatauwehea atu te kīanga pātahi y-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y-9\right)\left(6y+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$y\left(y-9\right)\left(6y+1\right)$$

Aromātai

$$y\left(y-9\right)\left(6y+1\right)$$