Whakaoti i te 16x^6+24x^5+5x^4

$$16 x ^ { 6 } + 24 x ^ { 5 } + 5 x ^ { 4 }$$

Tauwehe

$$\left(4x+1\right)\left(4x+5\right)x^{4}$$

Ngā Upane Otinga

Tauwehea te x^{4}.

$$x^{4}\left(16x^{2}+24x+5\right)$$

Whakaarohia te 16x^{2}+24x+5. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 16x^{2}+ax+bx+5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=24 ab=16\times 5=80$$

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 80.

$$1,80 2,40 4,20 5,16 8,10$$

Tātaihia te tapeke mō ia takirua.

$$1+80=81 2+40=42 4+20=24 5+16=21 8+10=18$$

Ko te otinga te takirua ka hoatu i te tapeke 24.

$$a=4 b=20$$

Tuhia anō te 16x^{2}+24x+5 hei \left(16x^{2}+4x\right)+\left(20x+5\right).

$$\left(16x^{2}+4x\right)+\left(20x+5\right)$$

Tauwehea te 4x i te tuatahi me te 5 i te rōpū tuarua.

$$4x\left(4x+1\right)+5\left(4x+1\right)$$

Whakatauwehea atu te kīanga pātahi 4x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(4x+1\right)\left(4x+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x^{4}\left(4x+1\right)\left(4x+5\right)$$

Aromātai

$$\left(4x+1\right)\left(4x+5\right)x^{4}$$