Question

Consider the Polynomial P(x)=x^3-5x^2-x+5. is (x-5) a factor?

a No, the remainder is 0, so x-5 is not a factor of P(x)

b Yes, the remainder is 0, so x-5 is a factor of P(x)

c Yes, the remainder is -240, so x-5 is a factor of P(x)

d No, the remainder is -240, so x-5 is not a factor of P(x)

Answer 1

Option B, Yes, the remainder is 0, so x-5 is a factor of P(x)

Explanation:

Step 1: Factor

p(x) = x^3 - 5x^2 - x + 5

p(x) = (x - 5)(x + 1)(x - 1)

Yes, the remainder is 0 so, x-5 is a factor of p(x)

Answer: Option B, Yes, the remainder is 0, so x-5 is a factor of P(x)