Which expression is a factor of both \( x^{2}-9 \) and \( x^{2}+8 x+15 ? \) \( (x+5) \)

To find a common factor of \( x^{2}-9 \) and \( x^{2}+8x+15 \), we can factor both expressions. The expression \( x^{2}-9 \) is a difference of squares, which factors to \( (x-3)(x+3) \). The expression \( x^{2}+8x+15 \) factors to \( (x+3)(x+5) \). Noticing that both factorizations share the common factor \( (x+3) \), we conclude that \( (x+3) \) is indeed a factor of both expressions. To check your understanding of factoring, remember that identifying the greatest common factor can simplify problem-solving significantly. A common mistake is assuming that expressions without obvious common terms don’t have shared factors—always explore the algebra!