To simplify the expression \(3x^2 + 2x - 5x - 2x^2 + 2\), we first combine like terms:
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Combine the \(x^2\) terms: \[ 3x^2 - 2x^2 = x^2 \]
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Combine the \(x\) terms: \[ 2x - 5x = -3x \]
So the expression simplifies to: \[ x^2 - 3x + 2 \]
Next, we will factor this quadratic expression. We need to find two numbers that multiply to \(2\) (the constant term) and add to \(-3\) (the coefficient of \(x\)). The numbers \(-1\) and \(-2\) fit this requirement, as: \[ -1 \times -2 = 2 \quad \text{and} \quad -1 + -2 = -3 \]
Thus, we can factor the expression as: \[ (x - 1)(x - 2) \]
Now let's compare this to the provided options. Since there is no \((x - 1)(x - 2)\) option present, we'll take a closer look at the given choices.
None of the choices seem to match what we obtained from factoring \(x^2 - 3x + 2\), which would imply that other options are incorrect based on your question.
The correct factoring should lead to: \[ \text{Factored form of } x^2 - 3x + 2 \text{ is } (x-1)(x-2). \]
Please check the options provided again to verify their accuracy. If we were to determine it based on the common factors, it doesn't match any of the selections you presented.
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