SOLUTION: Find the values of h and k given that x + 2 is a factor of Q(x) = (x + h)^2 + k, and the remainder is 16 when Q (x) is divided by x.

Q(x) =  = .


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) = .    (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 =  = 5.


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

    5^2 + k = 16,

    25 + k = 16,

         k = 16 - 25 = -9.


ANSWER.  h= 5;  k= = -9.