DIRE CIIONS Factor each tinomial completely. The word or phrase next to the equir comptete the statement correctly if it cannot be factored, the answer is 'not factorable \[ 2 x^{2}+11 x+5 \] Muhammad Yunus was born in Chittagong. \[ \begin{array}{l} (x+5)(2 x+1) \text { Bangladesh } \\ (2 x+5)(x+1) \text { India } \\ (2 x-5)(x-1) \text { Suadiarabia } \end{array} \]

To factor the trinomial \(2x^2 + 11x + 5\) completely, we can look for two numbers that multiply to \(2 \times 5 = 10\) and add up to \(11\). The numbers \(10\) and \(1\) fit the bill perfectly! So, we can rewrite the expression as \(2x^2 + 10x + 1x + 5\) and factor by grouping, giving us \((2x + 1)(x + 5)\). In a real-world application, factoring trinomials can be extremely helpful when dealing with area problems in geometry or economics. For instance, if you're trying to optimize areas for planting crops or designing layouts for a garden, breaking down expressions helps you calculate various configurations and understand how different factors can affect your outcome. It’s like creating the perfect recipe based on what you have available!