Whakaoti i te -5z-34+21z^2-45z+83z+z^3-42z^2+5=

$$-5z-34+21 { z }^{ 2 } -45z+83z+ { z }^{ 3 } -42 { z }^{ 2 } +5=$$

Aromātai

$$z^{3}-21z^{2}+33z-29$$

Ngā Upane Otinga

Pahekotia te -5z me -45z, ka -50z.

$$-50z-34+21z^{2}+83z+z^{3}-42z^{2}+5$$

Pahekotia te -50z me 83z, ka 33z.

$$33z-34+21z^{2}+z^{3}-42z^{2}+5$$

Pahekotia te 21z^{2} me -42z^{2}, ka -21z^{2}.

$$33z-34-21z^{2}+z^{3}+5$$

Tāpirihia te -34 ki te 5, ka -29.

$$33z-29-21z^{2}+z^{3}$$

Kimi Pārōnaki e ai ki z

$$3\left(z^{2}-14z+11\right)$$

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Tapeke

Pahekotia te -5z me -45z, ka -50z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-50z-34+21z^{2}+83z+z^{3}-42z^{2}+5)$$

Pahekotia te -50z me 83z, ka 33z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(33z-34+21z^{2}+z^{3}-42z^{2}+5)$$

Pahekotia te 21z^{2} me -42z^{2}, ka -21z^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(33z-34-21z^{2}+z^{3}+5)$$

Tāpirihia te -34 ki te 5, ka -29.

$$\frac{\mathrm{d}}{\mathrm{d}z}(33z-29-21z^{2}+z^{3})$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$33z^{1-1}+2\left(-21\right)z^{2-1}+3z^{3-1}$$

Tango 1 mai i 1.

$$33z^{0}+2\left(-21\right)z^{2-1}+3z^{3-1}$$

Whakareatia 2 ki te -21.

$$33z^{0}-42z^{2-1}+3z^{3-1}$$

Tango 1 mai i 2.

$$33z^{0}-42z^{1}+3z^{3-1}$$

Tango 1 mai i 3.

$$33z^{0}-42z^{1}+3z^{2}$$

Mō tētahi kupu t, t^{1}=t.

$$33z^{0}-42z+3z^{2}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$33\times 1-42z+3z^{2}$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$33-42z+3z^{2}$$