Question

1. a² - 4a - 24 + 6a

Explanation:

Step1: Combine like terms

First, we combine the like terms \(-4a\) and \(6a\) in the expression \(a^{2}-4a - 24+6a\).
\(-4a+6a = 2a\), so the expression becomes \(a^{2}+2a - 24\).

Step2: Factor the quadratic expression

We factor the quadratic expression \(a^{2}+2a - 24\). We need to find two numbers that multiply to \(- 24\) and add up to \(2\). The numbers are \(6\) and \(-4\) since \(6\times(-4)=-24\) and \(6+(-4) = 2\).
So we can write \(a^{2}+2a - 24=(a + 6)(a-4)\)

Answer:

\((a + 6)(a - 4)\) (or \(a^{2}+2a-24\) if we just simplify the original expression without factoring, but factoring is a common operation here)