Whakaoti i te 3x^3+3x+9-5x^3-7x^2+6-9=

$$3 { x }^{ 3 } +3x+9-5 { x }^{ 3 } -7 { x }^{ 2 } +6-9=$$

Aromātai

$$-\left(x-1\right)\left(2x^{2}+9x+6\right)$$

Ngā Upane Otinga

Pahekotia te 3x^{3} me -5x^{3}, ka -2x^{3}.

$$-2x^{3}+3x+9-7x^{2}+6-9$$

Tāpirihia te 9 ki te 6, ka 15.

$$-2x^{3}+3x+15-7x^{2}-9$$

Tangohia te 9 i te 15, ka 6.

$$-2x^{3}+3x+6-7x^{2}$$

Tauwehe

$$-2\left(x-1\right)\left(x-\frac{-\sqrt{33}-9}{4}\right)\left(x-\frac{\sqrt{33}-9}{4}\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$-2x^{3}-7x^{2}+3x+6$$

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 6, ā, ka wehea e q te whakarea arahanga -2. Ko tetahi pūtake pērā ko 1. Tauwehea te pūrau mā te whakawehe mā te x-1. Kāore te pūrau -2x^{2}-9x-6 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$\left(x-1\right)\left(-2x^{2}-9x-6\right)$$