Whakaoti i te 2x^3-10x^2+11x-7=(x-4)(2x^2+hx+3)+k

$$2 x ^ { 3 } - 10 x ^ { 2 } + 11 x - 7 = ( x - 4 ) ( 2 x ^ { 2 } + h x + 3 ) + k$$

Whakaoti mō h

$$\left\{\begin{matrix}h=-\frac{2x^{2}-8x+k-5}{x\left(x-4\right)}\text{, }&x\neq 4\text{ and }x\neq 0\\h\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=4\right)\text{ and }k=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x-4 ki te 2x^{2}+hx+3.

$$2x^{3}-10x^{2}+11x-7=2x^{3}+hx^{2}+3x-8x^{2}-4hx-12+k$$

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

$$2x^{3}+hx^{2}+3x-8x^{2}-4hx-12+k=2x^{3}-10x^{2}+11x-7$$

Tangohia te 2x^{3} mai i ngā taha e rua.

$$hx^{2}+3x-8x^{2}-4hx-12+k=2x^{3}-10x^{2}+11x-7-2x^{3}$$

Pahekotia te 2x^{3} me -2x^{3}, ka 0.

$$hx^{2}+3x-8x^{2}-4hx-12+k=-10x^{2}+11x-7$$

Tangohia te 3x mai i ngā taha e rua.

$$hx^{2}-8x^{2}-4hx-12+k=-10x^{2}+11x-7-3x$$

Pahekotia te 11x me -3x, ka 8x.

$$hx^{2}-8x^{2}-4hx-12+k=-10x^{2}+8x-7$$

Me tāpiri te 8x^{2} ki ngā taha e rua.

$$hx^{2}-4hx-12+k=-10x^{2}+8x-7+8x^{2}$$

Pahekotia te -10x^{2} me 8x^{2}, ka -2x^{2}.

$$hx^{2}-4hx-12+k=-2x^{2}+8x-7$$

Me tāpiri te 12 ki ngā taha e rua.

$$hx^{2}-4hx+k=-2x^{2}+8x-7+12$$

Tāpirihia te -7 ki te 12, ka 5.

$$hx^{2}-4hx+k=-2x^{2}+8x+5$$

Tangohia te k mai i ngā taha e rua.

$$hx^{2}-4hx=-2x^{2}+8x+5-k$$

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

$$\left(x^{2}-4x\right)h=-2x^{2}+8x+5-k$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}-4x\right)h=5-k+8x-2x^{2}$$

Whakawehea ngā taha e rua ki te x^{2}-4x.

$$\frac{\left(x^{2}-4x\right)h}{x^{2}-4x}=\frac{5-k+8x-2x^{2}}{x^{2}-4x}$$

Mā te whakawehe ki te x^{2}-4x ka wetekia te whakareanga ki te x^{2}-4x.

$$h=\frac{5-k+8x-2x^{2}}{x^{2}-4x}$$

Whakawehe -2x^{2}+8x+5-k ki te x^{2}-4x.

$$h=\frac{5-k+8x-2x^{2}}{x\left(x-4\right)}$$

Whakaoti mō k

$$k=5+8x+4hx-2x^{2}-hx^{2}$$