Question 1132054
.
<pre>
This problem is to use the "Remainder theorem".



The Remainder theorem says that the binomial (x-a) is a factor of a polynomial

    f(x) = {{{a[0]*x^n + a[1]*x^(n-1) + ellipsis + a[n-1]*x + a[n]}}}

if and only if the value of "a" is the root of the polynomial f(x), i.e. f(a) = 0.



So, in your case, to show that (x-2) is a factor of the given polynomial 

    f(x) = {{{x^3 - 2x^2 - 4x + 8}}},

you need simply calculate


    f(5) = {{{2^3 - 2*2^2 - 4*2 + 8}}} = 8 - 8 - 8 + 8 = 0


and make sure that it is equal to zero.
</pre>

Solved.


--------------------------


See the lessons

&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 and the Remainder theorem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solved-problems-on-the-Remainder-theorem.lesson>Solved problems on the Remainder thoerem</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

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


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


Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.