SOLUTION: Solve each problem. 1. Find the value of k so that the remainder is 25 when kx²-x+1 is divided by x-3. 2.Find the value of k so that the remainder is -1 when 5x²+kx-25 is

(1)  Due to the Remainder theorem, this passage

         " the remainder is  25  when    is divided by  x-3 "

     means that the value of the polynomial is equal to 25  at  x = 3.



     So, we substitute x= 3 into the polynomial and equate it to 25.

     It gives us an equation   = 25,

     from which we find k


           9k - 3 + 1 = 25

           9k -2 = 25

           9k    = 25 + 2 = 27

            k             = 27/9 = 3.     ANSWER