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.

Question 1144428: 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.
Answer by ikleyn(52898) (Show Source): You can put this solution on YOUR website!
.


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.

Solved.

RELATED QUESTIONS
Let f(x)=3x^4 + 7x^3 + ax^2 + bx -14 where a and b are constants.If (x-1) is a factor of... (answered by josgarithmetic)

Let f(x)=3x^4 + 7x^3 + ax^2 + bx -14 where a and b are constants.If (x-1) is a factor of... (answered by Boreal)

what is the lowest minimum value for |-(x+h)^2+k|-q id h,k, and q are positive... (answered by ikleyn)

The cubic polynomial f(x) is such that the coefficient of x^3 is -1 and the roots of the... (answered by KMST)

The polynomial f(x)=x^3-x^2-6kx+4k^2 where k is a constant has (x-3)as a factor. Find the (answered by ikleyn)

Given (x^2+4x+8)divided by (x+k), find the values of k so that the remainder is 20.... (answered by lwsshak3)

Find the remainder when p(x) is divided by q(x), where p(x) = x^5 + 1 and q(x) = x^2 + x... (answered by CPhill)

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = x^2 + 2 and... (answered by ikleyn)

given that the remainder when f(x) is divided by (x-1) is equal to the remainder when... (answered by Edwin McCravy)