Question

Divide f(x) by d(x), and write a summary statement in the form indicated. f(x) = x^4 - 4x^3 + 2x^2 - 4x + 1; d(x) = x^2 + 1

Answers:

f(x) = (x^2 + 1)( x^2 + 4x + 1)

f(x) = (x^2 + 1)( x^2 - 4x + 1) + 12x + 3

f(x) = (x^2 + 1)( x^2 + 4x + 1) + 12x + 3 

f(x) = (x^2 + 1)( x^2 - 4x + 1)

Answer 1

`(f(x))/(d(x))=(x^4 - 4x^3 + 2x^2 - 4x + 1)/(x^2 + 1 )\\ (f(x))/(d(x))=(x^4 - 4x^3 + x^2 +x^2 - 4x + 1)/(x^2 + 1 )\\ (f(x))/(d(x))=(x^4 + x^2 -4x^3-4x+x^2 + 1)/(x^2 + 1 )\\ (f(x))/(d(x))=(x^2(x^2+1)-4x(x^2+1)+1(x^2+1))/(x^2 + 1 )\\ (f(x))/(d(x))=((x^2+1)(x^2-4x+1))/(x^2 + 1 )\\ (f(x))/(d(x))=x^2-4x+1`