f(x) = x³ - 2x² - 24x
x³ - 2x² - 24x = 0
x(x² - 2x - 24) = 0
x = 0
x² - 2x - 24 = 0
a = 1, b = -2, c = -24
Delta = (-2)² - 4 * 1 * (-24) = 4 + 96 = 100
x = (-(-2) - 10)/(2 * 1) = -8/2 = -4
x = (-(-2) + 10)/(2 * 1) = 12/2 = 6
Answer: 2)
 
        
             
        
        
        
All that is needed is a single counter-example. 
One counter-example is to multiply the monomial x^3 with the binomial x^7-10x^4
We then get...
x^3*(x^7-10x^4) = x^3*x^7 + x^3*(-10x^4)
x^3*(x^7-10x^4) = x^10 - x^7
The result we get is a binomial as there are still only two terms here. We would need three terms to have a trinomial.