Question 1092470
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<pre>
Apply the Remainder theorem.


The remainder theorem says that  


    if a polynomial f(x) is divided by a binomial (x-a), where "a" is a constant term (a number), 
    then the remainder is equal to the value of f(x) at x= a, i.e. f(a).


In your case  a = 2.  By y substituting x= 2 into f(x) you get

    f(2) = 2^3 -b*2^2 + 4*2 - 20 = 8 - 4b + 8 - 20 = -4b - 4.


Therefore, your equation to find "b" is

    -4b - 4 = -2    (since -2 is the remainder !)

which implies  4b = 2 - 4 = -2,   b = {{{(-2)/4}}} = -0.5.
</pre>

<U>Answer</U>.  b = -0.5.


Solved.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Do the other cases in the same way.



----------------
On the Remainder theorem 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?content_action=edit_dev>Divisibility of polynomial f(x) by binomial x-a</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>".