A polynomial f(x) with real coefficients and leading coefficient 1 has zeros -7, 0, 1 + i and degree 4. Express f(x) as a product of linear and quadratic polynomials with real coefficients that are irreducible over IR. (Another one, I tried but it didn't work)

Question

anonymous · Answer

f(x)= x(x+7)(x -1- i)(x -1 +i )
f(x) = x(x+7)[(x-1)^2 - i^2]
f(x)= x(x+7)[(x-1)^2 +1) 
f(x)= x(x+7)(x^2 -2x +1 +1)
f(x) x(x+7)(x^2 -2x +2)

anonymous · Answer

Thanks!

anonymous · Answer

its probably a lack of brackets in your working out that is causing the mistakes lol

anonymous · Answer

Probably :)

anonymous · Answer

yes, bracket is pretty important here :D

anonymous · Answer

if 1+i is a root then so is 1-i

anonymous · Answer

f(x) = z (z-+7)(z - (1+i) ) (x- (1-i) )

anonymous · Answer

you probably need to put the brackets inside brackets , im guessing you are forgetting a minus sign when expanding

anonymous · Answer

why did I put z and x :|

anonymous · Answer

Yep, that's where it went wrong!

anonymous · Answer

lol lol, z and x...variables are always painful, we don't want more of that :D