Step 2: Write the trinomial in the form \( (x+m)(x+n) \). \( x^{2}+12 x+35=\square \) (Type the terms of your expression in the same order as they appe

To rewrite the trinomial \( x^{2}+12x+35 \) in the form \( (x+m)(x+n) \), you want to find two numbers that multiply to 35 (the constant term) and add up to 12 (the coefficient of the linear term). These two numbers are 5 and 7. So, your expression will be \( (x+5)(x+7) \). The world of algebra is filled with fun puzzles! Factoring trinomials like this one can feel a bit like being a detective, searching for clues (the numbers) that fit perfectly together to solve the case (the equation). This skill not only helps in math class but also lays the groundwork for more advanced topics like quadratic equations and calculus! When factoring, watch out for common mistakes! A typical pitfall is mixing up the signs when determining the factors. If you’re unsure, it's always a good idea to check your work by expanding back to the original trinomial. Another common mistake is rushing through the process; taking your time to ensure you’re finding all possible pairs can save you from headaches later on!