Whakaoti i te -12x^2-48x-36

$$-12 { x }^{ 2 } -48x-36$$

Tauwehe

$$-12\left(x+1\right)\left(x+3\right)$$

Ngā Upane Otinga

Tauwehea te 12.

$$12\left(-x^{2}-4x-3\right)$$

Whakaarohia te -x^{2}-4x-3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=-\left(-3\right)=3$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=-3$$

Tuhia anō te -x^{2}-4x-3 hei \left(-x^{2}-x\right)+\left(-3x-3\right).

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

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

$$x\left(-x-1\right)+3\left(-x-1\right)$$

Whakatauwehea atu te kīanga pātahi -x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x-1\right)\left(x+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$12\left(-x-1\right)\left(x+3\right)$$

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.

$$-12x^{2}-48x-36=0$$

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.

$$x=\frac{-\left(-48\right)±\sqrt{\left(-48\right)^{2}-4\left(-12\right)\left(-36\right)}}{2\left(-12\right)}$$

Pūrua -48.

$$x=\frac{-\left(-48\right)±\sqrt{2304-4\left(-12\right)\left(-36\right)}}{2\left(-12\right)}$$

Whakareatia -4 ki te -12.

$$x=\frac{-\left(-48\right)±\sqrt{2304+48\left(-36\right)}}{2\left(-12\right)}$$

Whakareatia 48 ki te -36.

$$x=\frac{-\left(-48\right)±\sqrt{2304-1728}}{2\left(-12\right)}$$

Tāpiri 2304 ki te -1728.

$$x=\frac{-\left(-48\right)±\sqrt{576}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-\left(-48\right)±24}{2\left(-12\right)}$$

Ko te tauaro o -48 ko 48.

$$x=\frac{48±24}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$x=\frac{48±24}{-24}$$

Nā, me whakaoti te whārite x=\frac{48±24}{-24} ina he tāpiri te ±. Tāpiri 48 ki te 24.

$$x=\frac{72}{-24}$$

Whakawehe 72 ki te -24.

$$x=-3$$

Nā, me whakaoti te whārite x=\frac{48±24}{-24} ina he tango te ±. Tango 24 mai i 48.

$$x=\frac{24}{-24}$$

Whakawehe 24 ki te -24.

$$x=-1$$

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 -3 mō te x_{1} me te -1 mō te x_{2}.

$$-12x^{2}-48x-36=-12\left(x-\left(-3\right)\right)\left(x-\left(-1\right)\right)$$

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

$$-12x^{2}-48x-36=-12\left(x+3\right)\left(x+1\right)$$

Aromātai

$$-12\left(x+1\right)\left(x+3\right)$$