You're given with the polynomial function,
p(x) = x³ + 5x² - 2x - 24
and that x1 = 2
knowing that one root is 2 then you can say that the polynomial is having a factor of (x-2).
Since you are asked for the zeros then we'll have it as
0 = x³ + 5x² - 2x - 24
dividing the polynomial with the factor (x-2) you will have
[tex] \frac{x^3 + 5x^2 -2x - 24}{x-2} = x^2 + 7x + 12[/tex]
or you'll have the factors as
(x - 2)(x² + 7x + 12) = 0
factoring the quadratic expression you'll have:
(x - 2)(x + 3)(x + 4) = 0
so you'll have the zeros as:
x - 2=0
x = 2
x + 3 = 0
x = -3
x + 4 = 0
x = -4
