Whakaoti i te f(x)=x^2+6x+5

$$f ( x ) = x ^ { 2 } + 6 x + 5$$

Tauwehe

$$\left(x+1\right)\left(x+5\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\times 5=5$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=5$$

Tuhia anō te x^{2}+6x+5 hei \left(x^{2}+x\right)+\left(5x+5\right).

$$\left(x^{2}+x\right)+\left(5x+5\right)$$

Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.

$$x\left(x+1\right)+5\left(x+1\right)$$

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

$$\left(x+1\right)\left(x+5\right)$$

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.

$$x^{2}+6x+5=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 5}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times 5}}{2}$$

Whakareatia -4 ki te 5.

$$x=\frac{-6±\sqrt{36-20}}{2}$$

Tāpiri 36 ki te -20.

$$x=\frac{-6±\sqrt{16}}{2}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-6±4}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±4}{2} ina he tāpiri te ±. Tāpiri -6 ki te 4.

$$x=-\frac{2}{2}$$

Whakawehe -2 ki te 2.

$$x=-1$$

Nā, me whakaoti te whārite x=\frac{-6±4}{2} ina he tango te ±. Tango 4 mai i -6.

$$x=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$x=-5$$

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 -1 mō te x_{1} me te -5 mō te x_{2}.

$$x^{2}+6x+5=\left(x-\left(-1\right)\right)\left(x-\left(-5\right)\right)$$

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

$$x^{2}+6x+5=\left(x+1\right)\left(x+5\right)$$

Aromātai

$$\left(x+1\right)\left(x+5\right)$$