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) = x2 + 1

Answer 1

A) f(x) = (x^2 + 1)( x^2 + 4x + 1)
B) f(x) = (x^2 + 1)( x^2 - 4x + 1) + 12x + 3
C) f(x) = (x^2 + 1)( x^2 + 4x + 1) + 12x + 3
D) f(x) = (x^2 + 1)( x^2 - 4x + 1)

Answer 2

Factorise it:

x^4 + 4x^3 + x^2 - 4x - 2 = 0

(x^4 + x^2 - 2) + 4x(x^2 - 1)= 0

(x^2 + 2)(x^2 - 1) + 4x(x^2 - 1) = 0

(x^2 - 1)(x^2 + 4x + 2) = 0

(x + 1)(x - 1)(x^2 + 4x + 2)= 0

Now, x^2 + 4x + 2 is an irreducible factor. Hence, we either use the quadratic formula or make it equal a square root:

Quadratic formula

x = [-4 +/- root(16 - 8)]/2

x = [-4 +/- root8]/2

x = [-4 +/- 2root2]/2

x = -2 +/- root2

Square root method:

x^2 + 4x + 2 = 0

x^2 + 4x + 2 + 2 = 2

x^2 + 4x + 4 = 2

(x + 2)^2 = 2

x + 2 = +/- root2

x = -2 +/- root2

Therefore the roots are 1, -1, -2 + root2, -2 - root2
(-2 + root2 = -0.5858; -2 - root2 = -3.4142)

This is for f(x)

Source: http://answers.yahoo.com/question/index?qid=20100305233729AAd69OY

Answer 3

I'm confused.. Did you even divide?

Answer 4

no not really I used the quadratic formula

Answer 5

I have to divide.. I put the instructions up there. And it says the answer has to be in the form the answer choices are in.