Math 209College Mathematics II
posted by Sheryl .
How do you factor this completely:
x^3 + ax + 3a + 3x^2

You are in luck with this one. Two pairs of terms have x + 3 as a common factor.
x^3 + ax + 3a + 3x^2
= x^2(x + 3)+ a(x + 3)
= (x^2 + a)(x + 3)
= (x + ia)(x  ia)(x + 3)
(i is the square root of 1)
Two of the three roots are complex, for real a. 
X^3+ax+3a+3x^2
x^2+3x^2+ax+3a
x(x+3)+a(x+3)
(x+a)(x+3)
x= a, x= 3