Use the Factor Theorem to show that (x - 3) is a factor of the polynomial P(x) = x^5-3x^4+5x^3-15x^2-6x+18

P(3) = 0

Step-by-step explanation:

Factor Theorem is a consequence of Remainder Theorem.

Remainder Theorem states that if polynomial f(x) is divided by a binomial (x - a) then the remainder is f(a).

Factor Theorem states that if f(a) = 0, then the binomial (x - a) is a factor of f(x).

We have the polynomial

To prove that x-3 is a factor of P, we calculate P(3):

Thus, x-3 is a factor of P(x)

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5