\[ 0=(x+7)\left(x^{2}+1\right) \] Answer: \( \begin{array}{l}x=-7 \text { or } x=-1 \\ x=-7 \text { or } x=1 \text { or } x=-1 \\ x= \pm 1 \\ x=-7\end{array} \)

This equation reveals not just a solution but takes us back to the fundamental principles of algebra. The factorization method used here helps us uncover the roots of a polynomial equation efficiently, showing how we can break down complex expressions into simpler parts. Just picture it: the expression can be easily dissected to find those values of \( x \) that make the entire equation equal zero! Now, let’s think about the real-world applications. These types of equations frequently model situations in physics—like calculating the points when an object hits the ground after being thrown. Understanding these roots helps engineers ensure structures can withstand different forces, showing just how critical fundamental algebra is in creating the world around us!