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

Answer 1

( x^4 - 4 x³ + 2 x² - 4 x + 1 ) : ( x² + 1 ) = x² - 4 x + 1
- x^4 - x²
------------------------
- 4 x³ + x² - 4 x
4 x³ + 4 x
-----------------------
x² + 1
- x² - 1
----------------
R ( x ) = 0
( x^4 - 4 x³ + 2 x² - 4 x + 1) = ( x² + 1 ) ( x² - 4 x + 1 )