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To factor the quadratic expression \(2n^2 + 5n + 2\), we'll use the method of factoring by grouping. Here are the steps: 1. First, identify the coefficients: - \(a = 2\) - \(b = 5\) - \(c = 2\) 2. Calculate the product \(ac = 2 \cdot 2 = 4\). 3. We need to find two numbers that multiply to \(4\) (the product \(ac\)) and add up to \(5\) (the coefficient \(b\)). These numbers are \(4\) and \(1\). 4. Rewrite the middle term (\(5n\)) using these two numbers: \[ 2n^2 + 4n + 1n + 2 \] 5. Now, factor by grouping. Group the terms in pairs: \[ (2n^2 + 4n) + (1n + 2) \] 6. Factor out the common factor from each pair: \[ 2n(n + 2) + 1(n + 2) \] 7. Notice that \((n + 2)\) is a common factor in both terms: \[ (2n + 1)(n + 2) \] So, the factored form of the quadratic expression \(2n^2 + 5n + 2\) is \((2n + 1)(n + 2)\).

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