Question 1060404
.
<pre>
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.


<U>Answer</U>.  The remainder when f(x) is divided by g(x) is equal to 11.
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The "Remainder theorem states that the remainder of the division of a polynomial f(x)  by a linear polynomial  (x&#8722;a)  is equal to f(a).

<pre>
     (Wikipedia, https://en.wikipedia.org/wiki/Polynomial_remainder_theorem).
</pre>

See also the lesson  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>

in this site.



Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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