Question 1144428
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Q(x) = {{{(x+h)^2 + k}}} = {{{x^2 + 2hx + h^2 + k}}}.


The fact that this polynomial gives the remainder 16, when it is divided by x,  means that

    h^2 + k = 16.         (1)


Then the polynomial takes the form


    Q(x) = {{{x^2 + 2hx + 16}}}.    (2)


Next, we are given that (x+2) divides this polynomial.


It means that x= -2 is its root  (the Remainder Theorem).


Write this equation Q(-2) = 0.  Due to  (2),  it takes the form

    ((-2)^2 + 2h*(-2) + 16 = 0.


Simplify and find "h" :

     4     - 4h + 16 = 0,

             4h = 16 + 4

             4h = 20

              h = {{{20/4}}} = 5.


Now substitute this value  h= 5  into formula (1). You will get

    5^2 + k = 16,

    25 + k = 16,

         k = 16 - 25 = -9.


<U>ANSWER</U>.  h= 5;  k= = -9.
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Solved.