Factorise fully: \( 5.1 .1 \quad 2 x^{2}+6 x \)

To factorise the expression \( 2x^2 + 6x \), we can first take out the common factor, which is 2x. This gives us: \[ 2x(x + 3) \] Now, the expression is fully factorised as \( 2x(x + 3) \). For a bit of fun, did you know that factoring has been around since ancient civilizations? The Babylonians were already into solving quadratic equations back in 2000 BC! They had a geometric approach to problems similar to our modern algebraic methods. If you're applying this knowledge beyond the classroom, factorization is key in fields like engineering and computer science. Understanding how to break down polynomials can help you optimize functions, whether you're designing a bridge or creating algorithms. So, next time you factor, you're not just crunching numbers; you're building the future!