Determine constant k, so x-4 is a factor of polynomial

Question

Polynomial: 2x^4-7x^3+kx-10

Answer 1

Sarah, you could use synthetic division to set up an equation to solve for k.

 

  4     2     -7      0     k     -10

  

                 8      4    16  4k+64

     

        2       1      4    k+16   4k+54

 

 

 

Hence, the equation becomes

 

4k+54 = 0 to make x-4 be a factor of the polynomial.

    -54   -54

 

4k=-54  This implies k=-54/4 = -27/2

 

The polynomial is 2x^4-7x^3-27/2*x-10