SOLUTION: Find k when (x-4) is a factor of 2x^2-3x+k

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Question 1082514: Find k when (x-4) is a factor of 2x^2-3x+k
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!
Root of 4, remainder must be 0. 

Synthetic Division for root of 4:

4    |    2    -3    k
     |
     |         8    20
     |_________________________
         2     5    k+20



Answer by ikleyn(52872)   (Show Source): You can put this solution on YOUR website!
.
The fact that (x-4) is a factor of  is equivalent, due to the Remainder theorem, that x= 4 is the root 
of the polynomial p(x) = , i.e. P(4) = 0,  or

     = 0.


It implies 

     = 0,  or  32 - 12 + k = 0  --->  k = -20.


Answer.   k = -20.


On the Remainder theorem see the lesson Divisibility of polynomial f(x) by binomial x-a in this site.


---------------------
    The remainder theorem

    1. The remainder of division the polynomial    by the binomial    is equal to the value    of the polynomial. 

    2. The binomial    divides the polynomial    if and only if the value of    is the root of the polynomial  ,  i.e.  .

    3. The binomial    factors the polynomial    if and only if the value of    is the root of the polynomial  ,  i.e.  .
---------------------


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

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



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