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Use the factor thorem and a calculator to factor the polynomial g(x)= x^3-5x^2-5x-6?
I found that x-6 is a factor and x^2+x+1 is a factor. But either I'm having a major brian lapse or x^2+x+1 can't be factored out.
1 Answer
- Roger the MoleLv 71 decade agoFavorite Answer
You are right about both factors.
The remaining question is whether or not you want to allow complex factors. If not, you're done.
If so, you can factor x^2+x+1 like this:
x^2+x+1 = 0
x^2 + x + (1/4) + (3/4) = 0
x^2 + x + (1/4) = -3/4
(x + (1/2))^2 = -3/4
x + (1/2) = ± (i√3)/2, where i = √-1
x = -(1± i√3)/2
using the factor theorem, the remaining factors are:
(x + (1 + i√3)/2 )(x + (1 - (i√3)/2 )
