`f(x)=x^3-6x^2+2x-4,\ g(x)=1-2x`

Explanation

To find the remainder when \( f(x) = x^3 - 6x^2 + 2x - 4 \) is divided by \( g(x) = 1 - 2x \), we can use the Remainder Theorem. According to the theorem, the remainder of the division of a polynomial \( f(x) \) by \( x - a \) is equal to \( f(a) \).

### Step-by-Step Solution:

1. **Identify the divisor in standard form**:
The polynomial \( g(x) = 1 - 2x \) can be rearranged to the form \( -2x + 1 \). We can express it as \( x - \frac{1}{2} \) by factoring out \( -2 \):
\[
g(x) = -2(x - \frac{1}{2})
...