Question

Please help. Factor the polynomial function over the complex fraction.

f(x) = x^3+2x^2+5x+10

What I got so far; (x+2)(x^2+5) but I need to factor x^2+5 into a complex factor.

Answer 1

`(x + 2)(x + i√(5))(x - i√(5))`

Explanation:

You are correct so far.

This is how you factor the binomial x^2 + 5 using complex factors.

`x^2 + 5 =`

`= x^2 - (-5)`

Now factor as a difference of squares: a^2 - b^2 = (a + b)(a - b).

`= (x + √(-5))(x - √(-5))`

`= (x + i√(5))(x - i√(5))`