Question

Solve the polynomial equation by factoring. x^3+2x^2-9x-18=0

Answer 1

Answer:

This can be factored to (x + 3)(x - 3)(x + 2) = 0

So x is equal to 3, -3 and -2

Step-by-step 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