SOLUTION: Write {{{x^4 - 6x^2 - 27}}} as a product of linear factors and quadratic factors that are irreducible over the reals.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write {{{x^4 - 6x^2 - 27}}} as a product of linear factors and quadratic factors that are irreducible over the reals.      Log On


   

Question 90666: Write x%5E4+-+6x%5E2+-+27 as a product of linear factors and quadratic factors that are irreducible over the reals.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Write x%5E4+-+6x%5E2+-+27 as a product of linear factors 
and quadratic factors that are irreducible over the 
reals.

x%5E4+-+6x%5E2+-+27 can be factored as

%28x%5E2+-+9%29%28x%5E2+%2B+3%29

The first parentheses contains the difference of two
perfect squares and that can be factored over the reals,
as %28x-3%29%28x%2B3%29so we end up with

%28x+-+3%29%28x%2B3%29%28x%5E2+%2B+3%29

That's as far as it cvan be factored over the
reals.

Edwin