Whakaoti i te 2p^2-10p+8

$$2 p ^ { 2 } - 10 p + 8$$

Tauwehe

$$2\left(p-4\right)\left(p-1\right)$$

Ngā Upane Otinga

Tauwehea te 2.

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

Whakaarohia te p^{2}-5p+4. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei p^{2}+ap+bp+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=1\times 4=4$$

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 4.

$$-1,-4 -2,-2$$

Tātaihia te tapeke mō ia takirua.

$$-1-4=-5 -2-2=-4$$

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

$$a=-4 b=-1$$

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

$$\left(p^{2}-4p\right)+\left(-p+4\right)$$

Tauwehea te p i te tuatahi me te -1 i te rōpū tuarua.

$$p\left(p-4\right)-\left(p-4\right)$$

Whakatauwehea atu te kīanga pātahi p-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(p-4\right)\left(p-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(p-4\right)\left(p-1\right)$$

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.

$$2p^{2}-10p+8=0$$

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.

$$p=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\times 8}}{2\times 2}$$

Pūrua -10.

$$p=\frac{-\left(-10\right)±\sqrt{100-4\times 2\times 8}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$p=\frac{-\left(-10\right)±\sqrt{100-8\times 8}}{2\times 2}$$

Whakareatia -8 ki te 8.

$$p=\frac{-\left(-10\right)±\sqrt{100-64}}{2\times 2}$$

Tāpiri 100 ki te -64.

$$p=\frac{-\left(-10\right)±\sqrt{36}}{2\times 2}$$

Tuhia te pūtakerua o te 36.

$$p=\frac{-\left(-10\right)±6}{2\times 2}$$

Ko te tauaro o -10 ko 10.

$$p=\frac{10±6}{2\times 2}$$

Whakareatia 2 ki te 2.

$$p=\frac{10±6}{4}$$

Nā, me whakaoti te whārite p=\frac{10±6}{4} ina he tāpiri te ±. Tāpiri 10 ki te 6.

$$p=\frac{16}{4}$$

Whakawehe 16 ki te 4.

$$p=4$$

Nā, me whakaoti te whārite p=\frac{10±6}{4} ina he tango te ±. Tango 6 mai i 10.

$$p=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$p=1$$

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 4 mō te x_{1} me te 1 mō te x_{2}.

$$2p^{2}-10p+8=2\left(p-4\right)\left(p-1\right)$$

Aromātai

$$2\left(p-4\right)\left(p-1\right)$$