Mathias found the product \( \frac{4 x+8}{x} \cdot \frac{5}{x+2} \) as follows. \( \frac{4 x+8}{x} \cdot \frac{5}{x+2}=\frac{4 x+18}{x} \cdot \frac{5}{x+2}=\frac{12}{1} \cdot \frac{5}{x+2}=\frac{60}{x+2} \) Which of the following best describes his error? He did not multiply the denominators correctly. He did not factor the first numerator. He did not divide out the 2 from the 4 and the 8 . He did not distribute the 5 to the terms in the other numerator:

Mathias made an error when manipulating the first numerator. The expression \(4x + 8\) can be factored as \(4(x + 2)\), but he did not do so. This oversight caused him to miss simplifying \(\frac{4(x + 2)}{x}\) alongside the \(\frac{5}{x + 2}\), which could have led to a cancellation of \(x + 2\) in the denominator. After factoring, it becomes much clearer! If he had factored \(4(x + 2)\), the expression \(\frac{4(x+2)}{x} \cdot \frac{5}{x+2}\) would simply cancel out the \(x + 2\) terms, ultimately streamlining his path to the final answer. Understanding factoring in algebra opens doors to easier calculations!