Divide the polynomial \(3x^3 - 2x^2 + 5x - 7\) by the polynomial \(x - 2\).

Step 1 ：Set up the long division, \(\frac{3x^3 - 2x^2 + 5x - 7}{x - 2}\)

Step 2 ：Divide the first term in the numerator by the first term in the denominator: \(\frac{3x^3}{x}\) gives 3x^2. Write this term above the division line.

Step 3 ：Multiply \(x - 2\) by 3x^2 to get \(3x^3 - 6x^2\), write this below \(3x^3 - 2x^2\) and subtract to get \(4x^2\). Bring down the next term to get \(4x^2 + 5x\).

Step 4 ：Divide the first term in the numerator by the first term in the denominator: \(\frac{4x^2}{x}\) gives 4x. Write this above the division line next to 3x^2.

Step 5 ：Multiply \(x - 2\) by 4x to get \(4x^2 - 8x\), write this below \(4x^2 + 5x\) and subtract to get \(13x\). Bring down the next term to get \(13x - 7\).

Step 6 ：Divide the first term in the numerator by the first term in the denominator: \(\frac{13x}{x}\) gives 13. Write this above the division line next to 4x.

Step 7 ：Multiply \(x - 2\) by 13 to get \(13x - 26\), write this below \(13x - 7\) and subtract to get \(19\).