Please help
Divide f(x) by d(x), and write a summary statement in the form indicated.
$\dfrac{x^4-4x^3+2x^2-4x+1}{x^2+1}$

Question

Please help
Divide f(x) by d(x), and write a summary statement in the form indicated.
$\dfrac{x^4-4x^3+2x^2-4x+1}{x^2+1}$

phi · Answer

see http://www.khanacademy.org/math/algebra2/polynomial_and_rational/dividing_polynomials/v/polynomial-division also, write you bottom as x^2 + 0x + 1 when you do this problem

sleepyjess · Answer

Thank you!

sleepyjess · Answer

I came up with $x^2-4x+1$ but it wants one of these as the answer
$f(x) = (x^2 + 1)( x^2 + 4x + 1)$
$f(x) = (x^2 + 1)( x^2 - 4x + 1) + 12x + 3$
$f(x) = (x^2 + 1)( x^2 + 4x + 1) + 12x + 3$
$f(x) = (x^2 + 1)( x^2 - 4x + 1)$

sleepyjess · Answer

@phi

phi · Answer

did it divide evenly?

sleepyjess · Answer

yes there was no remainder

phi · Answer

you found
f(x) / d(x) =  x^2−4x+1
if we multiply both sides by d(x) we get
f(x) = d(x)(x^2−4x+1)

d(x) is short for the denominator  (x^2+1)

phi · Answer

refresh your browser if not clear.

sleepyjess · Answer

So it would be the last option?

phi · Answer

yes