Divite \( 3 x^{2}-7 x+2 \) by \( 3 x-1 \)

To divide \( 3x^{2} - 7x + 2 \) by \( 3x - 1 \), you can use polynomial long division. First, divide the leading term of the numerator \( 3x^2 \) by the leading term of the denominator \( 3x \), which gives you \( x \). Then multiply \( x \) by \( 3x - 1 \) to get \( 3x^2 - x \). Subtract this result from the original polynomial: \[ (3x^2 - 7x + 2) - (3x^2 - x) = -6x + 2 \] Next, divide the new leading term \( -6x \) by the leading term \( 3x \), yielding \( -2 \). Multiply \( -2 \) by \( 3x - 1 \) to get \( -6x + 2 \). Subtract again: \[ (-6x + 2) - (-6x + 2) = 0 \] Therefore, the result of the division is: \[ x - 2 \] So, \( \frac{3 x^2 - 7 x + 2}{3 x - 1} = x - 2 \).