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To factor the quadratic expression \( 2v^2 + 11v + 5 \), we need to find two numbers whose product is \(2 \cdot 5 = 10\) and whose sum is \(11\). Let's identify the numbers: - Considering the numbers 1 and 10, we see that \(1 \cdot 10 = 10\) and \(1 + 10 = 11\). We can now rewrite the middle term (11v) using these two numbers: \[ 2v^2 + 11v + 5 = 2v^2 + v + 10v + 5 \] Next, we group the terms in pairs: \[ (2v^2 + v) + (10v + 5) \] We then factor out the greatest common factor from each pair: \[ v(2v + 1) + 5(2v + 1) \] Now, we factor out the common binomial factor \( (2v + 1) \): \[ (2v + 1)(v + 5) \] Thus, the factorized form of the quadratic expression \( 2v^2 + 11v + 5 \) is: \[ (2v + 1)(v + 5) \]

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