Whakaoti i te -5x^3+13x^2-6x

$$- 5 x ^ { 3 } + 13 x ^ { 2 } - 6 x$$

Tauwehe

$$x\left(2-x\right)\left(5x-3\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(-5x^{2}+13x-6\right)$$

Whakaarohia te -5x^{2}+13x-6. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -5x^{2}+ax+bx-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=13 ab=-5\left(-6\right)=30$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 30.

$$1,30 2,15 3,10 5,6$$

Tātaihia te tapeke mō ia takirua.

$$1+30=31 2+15=17 3+10=13 5+6=11$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=10 b=3$$

Tuhia anō te -5x^{2}+13x-6 hei \left(-5x^{2}+10x\right)+\left(3x-6\right).

$$\left(-5x^{2}+10x\right)+\left(3x-6\right)$$

Tauwehea te 5x i te tuatahi me te -3 i te rōpū tuarua.

$$5x\left(-x+2\right)-3\left(-x+2\right)$$

Whakatauwehea atu te kīanga pātahi -x+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+2\right)\left(5x-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x\left(-x+2\right)\left(5x-3\right)$$

Aromātai

$$x\left(2-x\right)\left(5x-3\right)$$