factonse \( 4 x^{2}+11 x+6 \)

To factor the quadratic expression \( 4x^{2}+11x+6 \), we look for two numbers that multiply to \( 4 \times 6 = 24 \) and add up to \( 11 \). Those numbers are \( 3 \) and \( 8 \). We can break down the middle term and factor by grouping: First, rewrite: \( 4x^{2} + 3x + 8x + 6 \). Now, group: \( (4x^{2} + 3x) + (8x + 6) \). Factoring out the common terms: \( x(4x + 3) + 2(4x + 3) \). Combine the groups: \( (4x + 3)(x + 2) \). So, the factored form is \( (4x + 3)(x + 2) \)! Want to see it visually? Imagine a treasure map where \( 4x + 3 \) and \( x + 2 \) are your treasure chests just waiting to be opened with the correct keys! Just plug in values and “unlock” the simplified treasures! You can apply this factoring technique in real life too! Think of it as breaking down a task. For example, when organizing a party, you can break down the tasks into smaller steps (inviting friends, buying snacks, planning games) to make it all easier. Just like with factoring, approaching a larger project with smaller components can help keep the chaos at bay!