Joshua wants to know if x−5 is a factor of the polynomial P(x)=x^3−5x^2−x+5. Joshua calculates P(5) and applies the Factor Theorem to conclude that x−5 is not a factor of P(x).

Question

Is Josh's conclusion that x−5 is not a factor correct? Why or why not?

a. No, the remainder is 0, therefore x−5 is a factor of P(x).

b. Yes, the remainder is 0, therefore x−5 is not a factor of P(x).

c. Yes, the remainder is −240, therefore x−5 is not a factor of P(x).

d. No, the remainder is −240, therefore x−5 is a factor of P(x).

please help I am very confused!

Answer 1

hard to say, since you don't say what the remainder is.
The Factor Theorem states that if the remainder is 0, then (x-5) is a factor of P(x).