Question

P(x)=9x3 - 54x2 + 6x - 27; (x - 6) Since the remainder is , (x-6) a factor. a) 0

b) 1
c) 27
d) 9

Answer 1

The Remainder Theorem is used to determine if (x - 6) is a factor of the polynomial by substituting x = 6 into the polynomial p(x). The remainder is zero, so (x - 6) is a factor of p(x). The correct answer is a) 0.

Step-by-step explanation:

The question asks whether (x - 6) is a factor of the polynomial p(x) = 9x^3 - 54x^2 + 6x - 27. To determine if (x - 6) is a factor, we check if the remainder is zero when we divide p(x) by (x - 6). This process is known as the Remainder Theorem, which states that if you substitute the value of x that makes (x - 6) zero into the polynomial and the result is also zero, then (x - 6) is indeed a factor of the polynomial.

Let's apply the Remainder Theorem by substituting x = 6 into p(x):

p(6) = 9(6)^3 - 54(6)^2 + 6(6) - 27
p(6) = 9(216) - 54(36) + 36 - 27
p(6) = 1944 - 1944 + 36 - 27
p(6) = 0

Since the remainder is zero, (x - 6) is indeed a factor of the polynomial p(x).

The answer to the student's question is a) 0.