Whakaoti i te 12-36k+15k^2

$$12 - 36 k + 15 k ^ { 2 }$$

Tauwehe

$$3\left(k-2\right)\left(5k-2\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(4-12k+5k^{2}\right)$$

Whakaarohia te 4-12k+5k^{2}. Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$5k^{2}-12k+4$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 5k^{2}+ak+bk+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-12 ab=5\times 4=20$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 20.

$$-1,-20 -2,-10 -4,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-20=-21 -2-10=-12 -4-5=-9$$

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

$$a=-10 b=-2$$

Tuhia anō te 5k^{2}-12k+4 hei \left(5k^{2}-10k\right)+\left(-2k+4\right).

$$\left(5k^{2}-10k\right)+\left(-2k+4\right)$$

Tauwehea te 5k i te tuatahi me te -2 i te rōpū tuarua.

$$5k\left(k-2\right)-2\left(k-2\right)$$

Whakatauwehea atu te kīanga pātahi k-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(k-2\right)\left(5k-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(k-2\right)\left(5k-2\right)$$

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.

$$15k^{2}-36k+12=0$$

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.

$$k=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 15\times 12}}{2\times 15}$$

Pūrua -36.

$$k=\frac{-\left(-36\right)±\sqrt{1296-4\times 15\times 12}}{2\times 15}$$

Whakareatia -4 ki te 15.

$$k=\frac{-\left(-36\right)±\sqrt{1296-60\times 12}}{2\times 15}$$

Whakareatia -60 ki te 12.

$$k=\frac{-\left(-36\right)±\sqrt{1296-720}}{2\times 15}$$

Tāpiri 1296 ki te -720.

$$k=\frac{-\left(-36\right)±\sqrt{576}}{2\times 15}$$

Tuhia te pūtakerua o te 576.

$$k=\frac{-\left(-36\right)±24}{2\times 15}$$

Ko te tauaro o -36 ko 36.

$$k=\frac{36±24}{2\times 15}$$

Whakareatia 2 ki te 15.

$$k=\frac{36±24}{30}$$

Nā, me whakaoti te whārite k=\frac{36±24}{30} ina he tāpiri te ±. Tāpiri 36 ki te 24.

$$k=\frac{60}{30}$$

Whakawehe 60 ki te 30.

$$k=2$$

Nā, me whakaoti te whārite k=\frac{36±24}{30} ina he tango te ±. Tango 24 mai i 36.

$$k=\frac{12}{30}$$

Whakahekea te hautanga \frac{12}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$k=\frac{2}{5}$$

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 2 mō te x_{1} me te \frac{2}{5} mō te x_{2}.

$$15k^{2}-36k+12=15\left(k-2\right)\left(k-\frac{2}{5}\right)$$

Tango \frac{2}{5} mai i k mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$15k^{2}-36k+12=15\left(k-2\right)\times \frac{5k-2}{5}$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 15 me te 5.

$$15k^{2}-36k+12=3\left(k-2\right)\left(5k-2\right)$$

Aromātai

$$3\left(k-2\right)\left(5k-2\right)$$