divide 6x^4+2x^3-6x^2-14x-1 by 3x+1 by using long divison show all work then explain if 3x+1 is a factor of the dividend

After working this problem out, we know that 3x + 1 is not a total factor of the dividend, because there is a remainder.

When you divide a polynomial by another polynomial, if there is a remainder, it is not a complete factor.

After dividing, we are left with: 2x^3 - 2x - 4 + (3 / (3x + 1))

There is a remainder of 3.