How are the binomial factors The trinomial \( x^{2}+7 x-18 \) fac (Factor completely)

To factor the trinomial \( x^{2}+7x-18 \), we need to find two numbers that multiply to \(-18\) (the constant term) and add up to \(7\) (the coefficient of \(x\)). Those numbers are \(9\) and \(-2\). Therefore, we can rewrite the trinomial as: \[ x^{2} + 9x - 2x - 18 \] Now, we can group the terms: \[ (x^{2} + 9x) + (-2x - 18) \] Factoring each group gives us: \[ x(x + 9) - 2(x + 9) \] Now, factor out the common binomial factor \((x + 9)\): \[ (x + 9)(x - 2) \] Thus, the complete factorization of the trinomial \( x^{2}+7x-18 \) is \((x + 9)(x - 2)\). For a fun fact, did you know that the trinomial could be visualized as a mini puzzle where you need to find the right pieces (numbers) to fit perfectly together? Just like a puzzle, every trinomial has its unique pair of factors waiting to be discovered! When dealing with factorizations like this, a common mistake is to mix signs; make sure to keep track of positive and negative numbers carefully. Double-check your multiplication and addition outcomes – it’s easy to overlook one little detail that can lead you astray!