Question

x square minus 4 is a factor of 10 x cube minus x square - 2 X + n. then find the value of 2 m + n

Answer 1

If a polynomial function f(x) is divisible by x - 2, then x-2 is a factor of f(x) and, by the Factor Theorem,  f(2) must equal zero.  

 

So, 2(2)3 + m(2)2 - 3 = 0

 

       16 + 4m - 3 = 0

 

               4m = -13     m = -13/4

 

Plugging 2 in for x and -13/4 for m into the second function and setting the result equal to zero, we get:       

   23 - 3(-13/4)(2)2 + 4n + 4 = 0

 

   8 +39 + 4n + 4 = 0

 

                     4n = -51

 

                      n = -51/4