Which are real zeroes of this function? x3 + 2x2 – 9x – 18

Try putting x = -2:-

f(-2)  =  -8 + 2(-2)^2 -9(-2) - 18 =   -8 + 8 + 18 -18 = 0

so one zero is  -2

as the  last term is -18 it is also worth trying  to see is  3 , -3  or 9 or -9   are roots   ( by the Rational Roots Theorem)

in fact f(3) = 0 and f(-3) = 0  also

So the real zeroes are -2,-3 and 3.