Whakaoti i te 3x^2-33x+72=

$$3 x ^ { 2 } - 33 x + 72 =$$

Tauwehe

$$3\left(x-8\right)\left(x-3\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(x^{2}-11x+24\right)$$

Whakaarohia te x^{2}-11x+24. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=1\times 24=24$$

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 24.

$$-1,-24 -2,-12 -3,-8 -4,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-24=-25 -2-12=-14 -3-8=-11 -4-6=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-8 b=-3$$

Tuhia anō te x^{2}-11x+24 hei \left(x^{2}-8x\right)+\left(-3x+24\right).

$$\left(x^{2}-8x\right)+\left(-3x+24\right)$$

Tauwehea te x i te tuatahi me te -3 i te rōpū tuarua.

$$x\left(x-8\right)-3\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(x-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(x-8\right)\left(x-3\right)$$

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.

$$3x^{2}-33x+72=0$$

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.

$$x=\frac{-\left(-33\right)±\sqrt{\left(-33\right)^{2}-4\times 3\times 72}}{2\times 3}$$

Pūrua -33.

$$x=\frac{-\left(-33\right)±\sqrt{1089-4\times 3\times 72}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-33\right)±\sqrt{1089-12\times 72}}{2\times 3}$$

Whakareatia -12 ki te 72.

$$x=\frac{-\left(-33\right)±\sqrt{1089-864}}{2\times 3}$$

Tāpiri 1089 ki te -864.

$$x=\frac{-\left(-33\right)±\sqrt{225}}{2\times 3}$$

Tuhia te pūtakerua o te 225.

$$x=\frac{-\left(-33\right)±15}{2\times 3}$$

Ko te tauaro o -33 ko 33.

$$x=\frac{33±15}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{33±15}{6}$$

Nā, me whakaoti te whārite x=\frac{33±15}{6} ina he tāpiri te ±. Tāpiri 33 ki te 15.

$$x=\frac{48}{6}$$

Whakawehe 48 ki te 6.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{33±15}{6} ina he tango te ±. Tango 15 mai i 33.

$$x=\frac{18}{6}$$

Whakawehe 18 ki te 6.

$$x=3$$

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 8 mō te x_{1} me te 3 mō te x_{2}.

$$3x^{2}-33x+72=3\left(x-8\right)\left(x-3\right)$$

Aromātai

$$3\left(x-8\right)\left(x-3\right)$$