Solve the equation: \( p^{2}+3 p=0 \) Answer: \( p= \) Write your answers as a list of integers or reduced fractions, with your answers separated by a comma. For example, if you get 4 and \( -\frac{2}{3} \) as your answers, then enter \( 4,-2 / 3 \) in the box. Question Help: Video

To solve the equation \( p^{2}+3p=0 \), we can factor it out. First, we notice that both terms share a common factor of \( p \): \[ p(p + 3) = 0 \] Setting each factor to zero gives us: 1. \( p = 0 \) 2. \( p + 3 = 0 \) which simplifies to \( p = -3 \) Thus, the solutions are \( p = 0 \) and \( p = -3 \). **Answer:** \( 0,-3 \) The polynomial was set to equal zero, and finding the roots through factoring is a classic method that dates back centuries, showcasing the beauty of algebra! When solving quadratic equations, it's easy to overlook that certain terms can factor into simpler forms. Common mistakes include missing the factorization options or miscalculating roots, so taking a moment to think creatively can help avoid errors!