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!