Find the remainder when \(2x^3 - 3x^2 + 4x - 5\) is divided by \(x - 2\).

Step 1 ：Step 1: Arrange the dividend and divisor in descending order of powers. So, we have \(2x^3 - 3x^2 + 4x - 5\) divided by \(x - 2\).

Step 2 ：Step 2: Divide the highest degree term in the dividend by the highest degree term in the divisor. Here, \(2x^3\) divided by \(x\) gives us \(2x^2\).

Step 3 ：Step 3: Multiply the entire divisor by the result from step 2 and subtract the result from the original dividend. \((x - 2) * 2x^2 = 2x^3 - 4x^2\). Subtracting this from the original dividend gives us \(x^2 + 4x - 5\).

Step 4 ：Step 4: Repeat the process starting from step 2 with the new dividend of \(x^2 + 4x - 5\). Divide \(x^2\) by \(x\) to get \(x\). Multiply the entire divisor by \(x\) to get \(x^2 - 2x\). Subtract this from the new dividend to get \(6x - 5\).

Step 5 ：Step 5: Repeat the process again with the new dividend of \(6x - 5\). Divide \(6x\) by \(x\) to get \(6\). Multiply the entire divisor by \(6\) to get \(6x - 12\). Subtract this from the new dividend to get \(7\), which is the remainder.