Divide the polynomial \(3x^3 - 5x^2 + 6x - 4\) by \(x - 2\)

Step 1 ：First, we set up the division: \[\frac{3x^3 - 5x^2 + 6x - 4}{x - 2}\].

Step 2 ：Next, we divide the first term of the numerator by the first term of the denominator: \[\frac{3x^3}{x} = 3x^2\]. This is the first term of our quotient.

Step 3 ：Then, we multiply \(3x^2\) by \(x - 2\), subtract this from \(3x^3 - 5x^2\), and bring down the next term (\(6x\)): \[(3x^3 - 5x^2) - (3x^2)(x - 2) + 6x = x^2 + 6x\].

Step 4 ：We repeat the process: divide \(x^2\) by \(x\) to get \(x\), multiply \(x\) by \(x - 2\) and subtract it from \(x^2 + 6x\), then bring down the last term (\(-4\)): \[(x^2 + 6x) - (x)(x - 2) - 4 = 4x - 4\].

Step 5 ：Finally, we divide \(4x\) by \(x\) to get \(4\), and multiply \(4\) by \(x - 2\) and subtract it from \(4x - 4\) to get 0.