what two numbers multiply to 24 and add to -10? -4 and -6 look good, so:
(x - 4)(x - 6)
x = 4 or 6
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X + 4 is a factor of x^3 + 3x^2 - 10x - 24 along with (x + 2) and (x - 3)
x2 - 10x - 24= x2 - 12x + 2x - 24= x(x - 12) + 2(x - 12)= (x - 12)(x + 2)
The equation x2 - 5x - 24 = 0 has the two solutions 8 and -3 for x.
x3 + 6x2 - 4x - 24 = (x + 6)(x2 - 4) = (x + 6)(x + 2)(x - 2)
2z+6z+24=0 8z+24=0 8z= -24 z= - 3