Find all solutions of the equation (real and/or imaginary) by factoring.
x^3+2x^2+5x+10=0
To factor the equation x^3 + 2x^2 + 5x + 10 = 0, we can start by setting up a synthetic division to test possible roots.
Let's start by testing x = -2:
-2 | 1 2 5 10
-2 | 1 0 5 -20
Since the remainder is not equal to 0, -2 is not a root.
Next, let's test x = 1:
1 | 1 2 5 10
1 | 1 3 8 18
Since the remainder is not equal to 0, 1 is not a root.
Thus, there are no rational roots for this equation. It looks like this equation cannot be factored by simple factorization techniques. Alternatively, we could use the cubic formula to find the roots.