Question 1092373
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According to the Remainder theorem, 


    if  f(x) gives the remainder -8  when is divided by (x-4),  then the value f(4) is equal to -8:  f(4) = -8.



So, from the condition, you have THIS  equation to find m:

    3*4^2 +m*4 + 4 = -8.


Simplify and solve for m:

    3*16 + 4m + 4 = -8  ====>  4m = -3*16 - 4 - 8  ====>  4m = -60  ====>  m = {{{-60/4}}} = -15.


<U>Answer</U>.  m = -15.
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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>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.



The first lesson contains the Remainder theorem (its formulation and the proof):


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    <B>Theorem</B> &nbsp;&nbsp;(the <B><I>remainder theorem</I></B>)

    <B>1</B>. The remainder of division the polynomial &nbsp;{{{f(x)}}}&nbsp; by the binomial &nbsp;{{{x-a}}}&nbsp; is equal to the value &nbsp;{{{f(a)}}}&nbsp; of the polynomial. 

    <B>2</B>. The binomial &nbsp;{{{x-a}}}&nbsp; divides the polynomial &nbsp;{{{f(x)}}}&nbsp; if and only if the value of &nbsp;{{{a}}}&nbsp; is the root of the polynomial &nbsp;{{{f(x)}}}, &nbsp;i.e. &nbsp;{{{f(a) = 0}}}.

    <B>3</B>. The binomial &nbsp;{{{x-a}}}&nbsp; factors the polynomial &nbsp;{{{f(x)}}}&nbsp; if and only if the value of &nbsp;{{{a}}}&nbsp; is the root of the polynomial &nbsp;{{{f(x)}}}, &nbsp;i.e. &nbsp;{{{f(a) = 0}}}.
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