how do you factor a polynomial that has nth degrees
Well, g(x) could initially be factored as:
g(x) = (x^2 - 7)(x^2 + 5)
The first term is factored as diff of squares:
(x + sqrt(7))(x - sqrt(7))
The second one involves i, or the sqrt(-1)
(x + i*sqrt(5))(x - i*sqrt(5))
When using foil, the last term would be:
(i*sqrt(5))*(-i*sqrt(5))
Group the terms:
-i^2 * [sqrt(5)]^2
-(-1)*5
5 So, it checks out.
The final polynomial is written as:
g(x) = [x + sqrt(7)]*[x - sqrt(7)]*[x + i*sqrt(5)]*[x - i*sqrt(5)]
Hope this helps