Concept:To find the roots of a cubic polynomial, test possible integer factors and factorise completely.Explanation:Let P(x)=x3−19x−30.Test x=5: P(5)=125−95−30=0.Therefore, (x−5) is a factor.Divide x3−19x−30 by (x−5) to obtain x2+5x+6.Factorise x2+5x+6=(x+2)(x+3).So x3−19x−30=(x−5)(x+2)(x+3).Set each factor equal to zero: x−5=0, x+2=0, x+3=0.Hence, the roots are x=5, x=−2, and x=−3.Answer:The roots are 5, −3, and −2, so the correct option is C.