What must be subtracted from `2x^(2)-3x+1` to get `x^(2)+x-2`?

Answer

To find what must be subtracted from \(2x^2 - 3x + 1\) to get \(x^2 + x - 2\), we can set up the equation as follows:

1. **Set up the equation**:
We want to find \(y\) such that:
\[ 2x^2 - 3x + 1 - y = x^2 + x - 2 \]

2. **Rearrange the equation**:
To find \(y\), we can rearrange the equation:
\[ y = 2x^2 - 3x + 1 - (x^2 + x - 2) \]

3. **Distribute the negative sign**:
Distributing the negative sign across the terms in the parentheses:
\[ y = 2x^2 - 3x + 1 - x^2 - x + 2 \]

4. **Combine like terms**:
Now, we combine the like terms:
- For \(x^2\) terms: \(2x^2 - x^2 = x^2\)
- For \(x\) terms: \(-3x - x = -4x\)
- For constant terms: \(1 + 2 = 3\)

So, we have:
\[ y = x^2 - 4x + 3 \]

5. **Final answer**:
Therefore, the expression that must be subtracted from \(2x^2 - 3x + 1\) to get \(x^2 + x - 2\) is:
\[ x^2 - 4x + 3 \]