Answer:
Step-by-step explanation:
-x is common to all three terms. Thus, -x^3-2x^2-3x = -x(x^2 + 2x + 3).
Use the quadratic formula to find the roots (and thus the factors) of
x^2 + 2x + 3: a = 1; b = 2; c = 3.
Thus, the discriminant is b^2-4ac, or 4 - 4(1)(3), or -8.
Because this discriminant is negative, x^2 + 2x + 3 has two complex, unequal roots. They are:
-2 ± i√8
x = -------------- or -1 ± i*2*√2
Thus, the three factors of the given polynomial are:
-x, (x + 1 + 2i√2), and (x + 1 - 2i√2)
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