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(3x^3+2x^2-5x+1)÷(3x+1)

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Kathleen, Unless your teacher gave you a misprint, this problem will have fractional coefficients. Most of these problems will have standard integral solutions(i.e. 2X^2 + 3X + 1). This one forces you to use fractions at the X position. I came up with X^2 + (1/3)X - (16/9)with a remainder of (25/9). When you begin each division step, a copy of the lead term must appear below the previous level, so that term can be cancelled out. After X^2 is used the next step shows X^2 - 5X ....Go ahead and try this. Since the divisor has a 3 in front, only (1/3)X can be used to guarantee the first column elimination. The third level comes up with (-16/3)X +1 from the last term brought down. That means that (-16/9) is needed for the final step! This suggests that either 3X + 1 is not a factor of the polynomial or that a mistake was made with the copy of the problem. Good Luck! Charles S of Arden, NC