Divide f(x) by d(x), and write a summary statement in the form indicated.

f(x) = x4 - 4x3 + 2x2 - 4x + 1; d(x) = x2 + 1

with how to solve this problem in detail is greatly appreciated

You will solve this by doing long division. You do this by putting x2 + 1/ x4 - 4x3 + 2x2 -4x + 1. Ok so what do you multipli by x2 to get x4? well you multiplyit by x2 now multiply x2 + 1 by x2 to get x4 + 1x4 now subtract this from the f(x) now you have  -4x3 + 3x2 - 4x + 1 now what do you need to multiply by x2 to get -4x3? well you would need -4x now multiply x2 + 1 to get -4x3 + -4x now subtract this from f(x).Thsi will give you 3x2 - 8x + 1. Ok now what do you need to multiply by x2 to get 3x2? well you would need only 3, now multiply 3 by x2 + 1 to get 3x2 + 3, now subtract it from f(x). now you are left with -8x + 4. Now can you divide anything that can be divided by x2 taht will give you -8x? NO because x2 has a bigger exponent than -8x. now with what you have left and your d(x) put them in a mix number to get x2 - 4x + 3 - 8x + 1/ x2 + 1... Hope this helped