Find the value of k in a quadratic equation

Question

Find the value of k so that the remainder is 14:

(x^2+kx-18)-(x-4)

PLEASE HELP!!!!!!!

 

Answer 1

P(x) = X^2 + KX -18

 

X^2 + KX - 18 = q(X) ( X- 4) +14     /  just like 17/4 = 4 ( 4) +1

                                                                     

It means that :

 

P( 4) = 14

 

Then:

  4^2 + 4K - 18 = 14

 

   4K - 2 = 14

 

    4k = 16

 

      k = 4

 

 

 

 

Answer 2

The remainder theorem states that the remainder when a polynomial P(x) is divided by x-a is P(a).

In your case the remainder when P(x)=x²+kx-18 is divided by x-4 is 14 or

P(4)=4²+4k-18=14 or 16+4k-18=14 or -2+4k=14 or 4k=16 or k=4