Factor: \( x^{2}+5 x \)

To factor the expression \( x^{2} + 5x \), you can start by identifying the common factor in both terms, which is \( x \). So, you can rewrite the expression as: \[ x(x + 5) \] Now, you have successfully factored the polynomial! This means that the solutions to the equation \( x^{2} + 5x = 0 \) can be found by setting each factor equal to zero: \( x = 0 \) or \( x + 5 = 0 \) (thus, \( x = -5 \)). To add a little twist, did you know that factoring is like playing detective? You’re looking for clues (the common factors) that help you break down a complex case (the polynomial) into simpler, manageable pieces. So next time you're at a party and someone mentions math, you can impress them with your factoring skills! Also, if you're ever stuck while factoring, a common mistake is to forget to factor out the greatest common factor (GCF) first. Double-checking for it can save you time and effort in the long run, and prevent potential errors when solving equations! Keeping your factoring game strong depends on that crucial first step.