Whakaoti i te {l}{3d^2-51d}{+126}

$$\left. \begin{array} { l } { 3 d ^ { 2 } - 51 d } \\ { + 126 } \end{array} \right.$$

Tauwehe

$$3\left(d-14\right)\left(d-3\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(d^{2}-17d+42\right)$$

Whakaarohia te d^{2}-17d+42. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei d^{2}+ad+bd+42. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-17 ab=1\times 42=42$$

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 42.

$$-1,-42 -2,-21 -3,-14 -6,-7$$

Tātaihia te tapeke mō ia takirua.

$$-1-42=-43 -2-21=-23 -3-14=-17 -6-7=-13$$

Ko te otinga te takirua ka hoatu i te tapeke -17.

$$a=-14 b=-3$$

Tuhia anō te d^{2}-17d+42 hei \left(d^{2}-14d\right)+\left(-3d+42\right).

$$\left(d^{2}-14d\right)+\left(-3d+42\right)$$

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

$$d\left(d-14\right)-3\left(d-14\right)$$

Whakatauwehea atu te kīanga pātahi d-14 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(d-14\right)\left(d-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(d-14\right)\left(d-3\right)$$

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.

$$3d^{2}-51d+126=0$$

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.

$$d=\frac{-\left(-51\right)±\sqrt{\left(-51\right)^{2}-4\times 3\times 126}}{2\times 3}$$

Pūrua -51.

$$d=\frac{-\left(-51\right)±\sqrt{2601-4\times 3\times 126}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$d=\frac{-\left(-51\right)±\sqrt{2601-12\times 126}}{2\times 3}$$

Whakareatia -12 ki te 126.

$$d=\frac{-\left(-51\right)±\sqrt{2601-1512}}{2\times 3}$$

Tāpiri 2601 ki te -1512.

$$d=\frac{-\left(-51\right)±\sqrt{1089}}{2\times 3}$$

Tuhia te pūtakerua o te 1089.

$$d=\frac{-\left(-51\right)±33}{2\times 3}$$

Ko te tauaro o -51 ko 51.

$$d=\frac{51±33}{2\times 3}$$

Whakareatia 2 ki te 3.

$$d=\frac{51±33}{6}$$

Nā, me whakaoti te whārite d=\frac{51±33}{6} ina he tāpiri te ±. Tāpiri 51 ki te 33.

$$d=\frac{84}{6}$$

Whakawehe 84 ki te 6.

$$d=14$$

Nā, me whakaoti te whārite d=\frac{51±33}{6} ina he tango te ±. Tango 33 mai i 51.

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

Whakawehe 18 ki te 6.

$$d=3$$

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 14 mō te x_{1} me te 3 mō te x_{2}.

$$3d^{2}-51d+126=3\left(d-14\right)\left(d-3\right)$$

Aromātai

$$3\left(d-14\right)\left(d-3\right)$$