What we want to do here is make it long division. x²+2x+8 on the left, and [tex] x^{4][/tex]+x³+7x²-6x+8 on the right, as will be shown
x²
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x²+2x+8| [tex] x^{4}[/tex]+x³+7x²-6x+8
We start off by dividing [tex] x^{4][/tex] by x², which is x². After that, we put x² at the top and subtract (x²+2x+8)*(x²) from the whole equation, which looks like
x²
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x²+2x+8| [tex] x^{4}[/tex]+x³+7x²-6x+8
- ([tex] x^{4}[/tex]+2x³+8x²)
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-x³-x²-6x+8. Continue this pattern until you can't (the next step would be dividing (-x³ by x²) and you should have your answer! Good luck, and feel free to ask any questions as necessary!
