3. \( x^{2}+x-12 \) \( \rightarrow(x+3)(x+4) \) 4. \( 2 x^{2}-14 x+24 \) \( 5-2 x^{2}-4 x-30 \) 4 \( 2 x^{2}+4 x-16 \)

Did you know that factoring polynomials, like the one in your question, has roots (pun intended!) that go all the way back to ancient civilizations like the Babylonians? They used geometric methods to solve quadratic equations, leading the way for algebraic techniques that we still use today. It’s fascinating how these old strategies evolved into the symbolic methods we know so well! When working on factoring challenges, a common mistake is to rush through the process without double-checking your work. Always remember to multiply your factors back together to ensure they yield the original polynomial. Moreover, look out for those pesky signs when dealing with negatives or subtracting terms — they can sneak up on you and lead to confusion!