Question

1. Divide 6x^4 + 2x^3 – 6x^2 – 14x – 1 by 3x + 1 by using synthetic division or long division. Show all
your work. Then explain if 3x + 1 is a factor of the dividend.
Is 3x + 1 a factor? ______ Why or why not?

Answer 1

                  2x^3 - 2x - 4

3x + 1        6x^4 + 2x^3 - 6x^2 - 14x - 1
                  6x^4 + 2x^3
                
                                       -6x^2 - 14x - 1
                                       -6x^2 - 2x
     
                                                 -12x - 1
                                                 -12x - 4
 
                                                           3

3x + 1 is not a factor of the dividend because, dividing the dividend with 3x + 1 gives a remainder.