To simplify the polynomial \((x^2 - 4x + 3) + (2x^2 + 2x - 1)\), we can combine like terms.
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First, let's group the terms based on their degrees:
- \(x^2\) terms: \(x^2 + 2x^2\)
- \(x\) terms: \(-4x + 2x\)
- Constant terms: \(3 - 1\)
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Now, let's perform the additions for each group:
- \(x^2\) terms: \(1x^2 + 2x^2 = 3x^2\)
- \(x\) terms: \(-4x + 2x = -2x\)
- Constant terms: \(3 - 1 = 2\)
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Now, let's put everything together:
\[ 3x^2 - 2x + 2 \]
Thus, the simplified polynomial in standard form is:
\[ \boxed{3x^2 - 2x + 2} \]
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