polynomials

[Princezz3286]

given that -1 is a zero factor of the polynomial g(x) = x^3 + 5x^2 +17x + 13 express g(x) as a product of linear factors.
can you please run through the steps with me on how to do this? does it involve factoring? Im a little rusty
THanks in advance!

 

[BigGlenntheHeavy]

\(\displaystyle g(x) \ = \ x^3+5x^2+17x+13\)

\(\displaystyle g(-1) \ = \ 0. \ hence \ x+1 \ is \ a \ factor \ of \ g(x).\)

\(\displaystyle Now. \ dividing \ (x+1) \ into \ g(x) \ gives \ (x+1)(x^2+4x+13)\)

\(\displaystyle Now, \ x^2+4x+13 \ is \ prime, \ however \ if \ we \ wish \ to \ delve \ into \ "imaginary \ land",\)

\(\displaystyle then \ we \ have \ g(x) \ = \ (x+1)[x+(2+3i)][x+(2-3i)].\)