Question

I don’t understand part B. Can someone please help me?!

Picture included

Answer 1

What we want to do here is make it long division. x²+2x+8 on the left, and
`x^{4]`+x³+7x²-6x+8 on the right, as will be shown


x²
________________________________________
x²+2x+8|
`x^(4)`+x³+7x²-6x+8


We start off by dividing
`x^{4]` 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
________________________________________
x²+2x+8|
`x^(4)`+x³+7x²-6x+8
- (
`x^(4)`+2x³+8x²)
_____________________
-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!