Whakaoti i te f(x)=-1/4x^3+11/4x^2-6x

$$f ( x ) = - \frac { 1 } { 4 } x ^ { 3 } + \frac { 11 } { 4 } x ^ { 2 } - 6 x$$

Tauwehe

$$\frac{x\left(3-x\right)\left(x-8\right)}{4}$$

Ngā Upane Otinga

Tauwehea te \frac{1}{4}.

$$\frac{-x^{3}+11x^{2}-24x}{4}$$

Whakaarohia te -x^{3}+11x^{2}-24x. Tauwehea te x.

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

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.

$$a+b=11 ab=-\left(-24\right)=24$$

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 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.

$$\frac{x\left(x-8\right)\left(-x+3\right)}{4}$$

Aromātai

$$\frac{x\left(3-x\right)\left(x-8\right)}{4}$$