Question

If a polynomial function f(x) has roots 1+√2 and -3, what must be a factor of f(x)?

Answer 1

If it has a root at -3, we know that (x + 3) is a guaranteed root, because to a root from a factor, you simply set the expression inside the parentheses equal to zero and solve for x.

(x + 3) = 0

x = -3

We do the same thing but in vice versa to find the factor.

x = -3

x + 3

Thus, the factor is (x + 3)