Question

Which of the following are roots of the polynomial function? Check all that apply.

F(x) = x3 - x2 - 5x - 3

Answer 1

Descarte's rule of signs tells you there is one positive real root. The only positive real number on the list is 3.

Using synthetic division to find the quotient when dividing x³-x²-5x-3 by (x-3), we find the quotient is x²+2x+1, which we recognize as (x+1)².

Thus, -1 is a root with multiplicity 2, and 3 is a root.

The selections that should be checked are A and B.