Whakaoti i te -3u^2-36u+135

$$- 3 u ^ { 2 } - 36 u + 135$$

Tauwehe

$$3\left(3-u\right)\left(u+15\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(-u^{2}-12u+45\right)$$

Whakaarohia te -u^{2}-12u+45. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -u^{2}+au+bu+45. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-12 ab=-45=-45$$

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 -45.

$$1,-45 3,-15 5,-9$$

Tātaihia te tapeke mō ia takirua.

$$1-45=-44 3-15=-12 5-9=-4$$

Ko te otinga te takirua ka hoatu i te tapeke -12.

$$a=3 b=-15$$

Tuhia anō te -u^{2}-12u+45 hei \left(-u^{2}+3u\right)+\left(-15u+45\right).

$$\left(-u^{2}+3u\right)+\left(-15u+45\right)$$

Tauwehea te u i te tuatahi me te 15 i te rōpū tuarua.

$$u\left(-u+3\right)+15\left(-u+3\right)$$

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

$$\left(-u+3\right)\left(u+15\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(-u+3\right)\left(u+15\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$-3u^{2}-36u+135=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$u=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\left(-3\right)\times 135}}{2\left(-3\right)}$$

Pūrua -36.

$$u=\frac{-\left(-36\right)±\sqrt{1296-4\left(-3\right)\times 135}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$u=\frac{-\left(-36\right)±\sqrt{1296+12\times 135}}{2\left(-3\right)}$$

Whakareatia 12 ki te 135.

$$u=\frac{-\left(-36\right)±\sqrt{1296+1620}}{2\left(-3\right)}$$

Tāpiri 1296 ki te 1620.

$$u=\frac{-\left(-36\right)±\sqrt{2916}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 2916.

$$u=\frac{-\left(-36\right)±54}{2\left(-3\right)}$$

Ko te tauaro o -36 ko 36.

$$u=\frac{36±54}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$u=\frac{36±54}{-6}$$

Nā, me whakaoti te whārite u=\frac{36±54}{-6} ina he tāpiri te ±. Tāpiri 36 ki te 54.

$$u=\frac{90}{-6}$$

Whakawehe 90 ki te -6.

$$u=-15$$

Nā, me whakaoti te whārite u=\frac{36±54}{-6} ina he tango te ±. Tango 54 mai i 36.

$$u=-\frac{18}{-6}$$

Whakawehe -18 ki te -6.

$$u=3$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te -15 mō te x_{1} me te 3 mō te x_{2}.

$$-3u^{2}-36u+135=-3\left(u-\left(-15\right)\right)\left(u-3\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$-3u^{2}-36u+135=-3\left(u+15\right)\left(u-3\right)$$

Aromātai

$$3\left(3-u\right)\left(u+15\right)$$