Answer:
This can be factored to (x + 3)(x - 3)(x + 2) = 0
So x is equal to 3, -3 and -2
Explanation:
x³ + 2x² - 9x -18 = 0
Let's try dividing by (x + 3) as that looks like it might be a factor. We'll use long division:
x² - x - 6
x + 3 } x³ + 2x² - 9x -18
x³ + 3x²
-x² - 9x
-x² - 3x
-6x - 18
-6x - 18
0
Perfect! So (x + 3) is a factor, giving us:
(x + 3)(x² - x - 6)
the remaining quadratic can be factored more easily:
(x + 3)(x² - x - 6)
= (x + 3)(x² + 2x - 3x - 6)
= (x + 3)(x[x + 2] - 3[x + 2])
= (x + 3)(x - 3)(x + 2)
Now we can solve it easily as we know that's equal to zero, so x can be equal to 3, -3, and -2