SOLUTION: f(x) = 2x^80 - 4x^70 + 2x^40 + 4x^33 - 2x^12 + 9 g(x) = x - 1 Find the remainder when f(x) is divided by g(x), without using division.

Algebra ->  Test -> SOLUTION: f(x) = 2x^80 - 4x^70 + 2x^40 + 4x^33 - 2x^12 + 9 g(x) = x - 1 Find the remainder when f(x) is divided by g(x), without using division.      Log On


   

Question 1060404: f(x) = 2x^80 - 4x^70 + 2x^40 + 4x^33 - 2x^12 + 9
g(x) = x - 1
Find the remainder when f(x) is divided by g(x), without using division.
Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
.
According to the "Remainder theorem", the remainder is f(1), i.e. the value of the given polynomial at x= 1:


f(1) = 2*1^80 - 4*1^70 + 2*1^40 + 4*1^33 - 2*1^12 + 9 = 

     = 2      - 4      + 2      + 4       - 2     + 9 = 11.


Answer.  The remainder when f(x) is divided by g(x) is equal to 11.
---------------------------

The "Remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial (x−a) is equal to f(a). 
     (Wikipedia, https://en.wikipedia.org/wiki/Polynomial_remainder_theorem).

See also the lesson
    - Divisibility of polynomial f(x) by binomial x-a
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".