Whakaoti i te 2x^2+16x+32+12x^3+48x^2-4x-16

$$2 x ^ { 2 } + 16 x + 32 + 12 x ^ { 3 } + 48 x ^ { 2 } - 4 x - 16$$

Aromātai

$$2\left(x+4\right)\left(6x^{2}+x+2\right)$$

Ngā Upane Otinga

Pahekotia te 2x^{2} me 48x^{2}, ka 50x^{2}.

$$50x^{2}+16x+32+12x^{3}-4x-16$$

Pahekotia te 16x me -4x, ka 12x.

$$50x^{2}+12x+32+12x^{3}-16$$

Tangohia te 16 i te 32, ka 16.

$$50x^{2}+12x+16+12x^{3}$$

Tauwehe

$$2\left(x+4\right)\left(6x^{2}+x+2\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(25x^{2}+6x+8+6x^{3}\right)$$

Whakaarohia te x^{2}+8x+16+6x^{3}+24x^{2}-2x-8. Whakarea ka paheko i ngā kīanga tau ōrite.

$$6x^{3}+25x^{2}+6x+8$$

Whakaarohia te 6x^{3}+25x^{2}+6x+8. Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 8, ā, ka wehea e q te whakarea arahanga 6. Ko tetahi pūtake pērā ko -4. Tauwehea te pūrau mā te whakawehe mā te x+4.

$$\left(x+4\right)\left(6x^{2}+x+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa. Kāore te pūrau 6x^{2}+x+2 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$2\left(x+4\right)\left(6x^{2}+x+2\right)$$