Whakaoti i te 2x^2-x+q-5=(2x+1)(x+p)

$$2 x ^ { 2 } - x + q - 5 = ( 2 x + 1 ) ( x + p )$$

Whakaoti mō p (complex solution)

$$\left\{\begin{matrix}p=-\frac{2x-q+5}{2x+1}\text{, }&x\neq -\frac{1}{2}\\p\in \mathrm{C}\text{, }&q=4\text{ and }x=-\frac{1}{2}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+1 ki te x+p.

$$2x^{2}-x+q-5=2x^{2}+2xp+x+p$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2x^{2}+2xp+x+p=2x^{2}-x+q-5$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$2xp+x+p=2x^{2}-x+q-5-2x^{2}$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$2xp+x+p=-x+q-5$$

Tangohia te x mai i ngā taha e rua.

$$2xp+p=-x+q-5-x$$

Pahekotia te -x me -x, ka -2x.

$$2xp+p=-2x+q-5$$

Pahekotia ngā kīanga tau katoa e whai ana i te p.

$$\left(2x+1\right)p=-2x+q-5$$

Whakawehea ngā taha e rua ki te 2x+1.

$$\frac{\left(2x+1\right)p}{2x+1}=\frac{-2x+q-5}{2x+1}$$

Mā te whakawehe ki te 2x+1 ka wetekia te whakareanga ki te 2x+1.

$$p=\frac{-2x+q-5}{2x+1}$$

Whakaoti mō p

$$\left\{\begin{matrix}p=-\frac{2x-q+5}{2x+1}\text{, }&x\neq -\frac{1}{2}\\p\in \mathrm{R}\text{, }&q=4\text{ and }x=-\frac{1}{2}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+1 ki te x+p.

$$2x^{2}-x+q-5=2x^{2}+2xp+x+p$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2x^{2}+2xp+x+p=2x^{2}-x+q-5$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$2xp+x+p=2x^{2}-x+q-5-2x^{2}$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$2xp+x+p=-x+q-5$$

Tangohia te x mai i ngā taha e rua.

$$2xp+p=-x+q-5-x$$

Pahekotia te -x me -x, ka -2x.

$$2xp+p=-2x+q-5$$

Pahekotia ngā kīanga tau katoa e whai ana i te p.

$$\left(2x+1\right)p=-2x+q-5$$

Whakawehea ngā taha e rua ki te 2x+1.

$$\frac{\left(2x+1\right)p}{2x+1}=\frac{-2x+q-5}{2x+1}$$

Mā te whakawehe ki te 2x+1 ka wetekia te whakareanga ki te 2x+1.

$$p=\frac{-2x+q-5}{2x+1}$$

Whakaoti mō q

$$q=2px+2x+p+5$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+1 ki te x+p.

$$2x^{2}-x+q-5=2x^{2}+2xp+x+p$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$-x+q-5=2x^{2}+2xp+x+p-2x^{2}$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$-x+q-5=2xp+x+p$$

Me tāpiri te x ki ngā taha e rua.

$$q-5=2xp+x+p+x$$

Pahekotia te x me x, ka 2x.

$$q-5=2xp+2x+p$$

Me tāpiri te 5 ki ngā taha e rua.

$$q=2xp+2x+p+5$$