Answer to Question #154077 in Algebra for fdfs

Question

. If f ( x) = x3 − 2 x2 − x + 5 , then the remainder of g ( x) = f ( f ( x)) divided by ( x − 2) is

Answer 1

According to polynomial reminder theorem, remainder of division of a polynomial p(x) by a linear polynomial x - a is equal to p(a).

Let p(x) = g(x), a = 2, r - remainder of g(x), divided by x - 2.

We have: r = g(2) = f(f(2)) = f(2³ - 2*2² - 2 + 5) = f(8 - 8 - 2 + 5) = f(3) = 3³ - 2*3² - 3 + 5 = 27 - 18 - 3 + 5 = 11

Answer: remainder is equal to 11.

References:

polynomial remainder theorem: https://en.wikipedia.org/wiki/Polynomial_remainder_theorem