Solving (x³  4x² + 6x  4) / (x  2) using Synthetic Division
Synthetic division is a shortcut method for dividing polynomials, particularly when the divisor is a linear expression in the form of (x  a). Let's walk through how to solve (x³  4x² + 6x  4) / (x  2) using synthetic division.
Steps for Synthetic Division

Set up the problem:
 Write the coefficients of the dividend (x³  4x² + 6x  4) in a row: 1 4 6 4
 Write the value of 'a' from the divisor (x  2) to the left of the coefficients: 2  1 4 6 4

Bring down the leading coefficient:
 Bring down the first coefficient (1) below the line. 2  1 4 6 4
 1

Multiply and add:
 Multiply the value 'a' (2) by the number you just brought down (1): 2 * 1 = 2
 Add the result (2) to the next coefficient (4): 4 + 2 = 2
 Write this result (2) below the line: 2  1 4 6 4
 1 2

Repeat steps 3 and 4:

Multiply the value 'a' (2) by the last number (2): 2 * 2 = 4

Add the result (4) to the next coefficient (6): 6  4 = 2

Write this result (2) below the line: 2  1 4 6 4

1 2 2

Multiply the value 'a' (2) by the last number (2): 2 * 2 = 4

Add the result (4) to the next coefficient (4): 4 + 4 = 0

Write this result (0) below the line: 2  1 4 6 4

1 2 2 0


Interpret the results:
 The last number (0) is the remainder.
 The other numbers (1 2 2) are the coefficients of the quotient, starting with the highest power of x (x²).
The Solution
Therefore, the quotient is x²  2x + 2 and the remainder is 0. This means that (x³  4x² + 6x  4) is perfectly divisible by (x  2), and the result is x²  2x + 2.