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To factor the quadratic expression \(5n^2 + 19n + 12\), we can use the method of factoring by grouping. Here are the detailed steps: 1. **Multiply the leading coefficient (5) by the constant term (12):** \(5 \times 12 = 60\). 2. **Find two numbers that multiply to 60 and add up to the middle coefficient (19):** The numbers that multiply to 60 and add up to 19 are 15 and 4. 3. **Rewrite the middle term (19n) using the two numbers found:** \(5n^2 + 15n + 4n + 12\). 4. **Group the terms in pairs:** \((5n^2 + 15n) + (4n + 12)\). 5. **Factor out the greatest common factor (GCF) from each pair:** \(5n(n + 3) + 4(n + 3)\). 6. **Factor out the common binomial factor:** \((n + 3)(5n + 4)\). So, the factored form of \(5n^2 + 19n + 12\) is \((n + 3)(5n + 4)\).

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