Question

adva unit 4b: quadratics solving review 1. solve by factoring: a. $x^2 + 2x - 24 = 0$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-24\) and add up to \(2\). Let's list the factor pairs of \(-24\): \((-4, 6)\) because \(-4\times6 = -24\) and \(-4 + 6 = 2\).

Step2: Factor the quadratic

Rewrite the middle term using these two numbers: \(x^{2}-4x + 6x - 24 = 0\). Then factor by grouping: \(x(x - 4)+6(x - 4)=0\), which simplifies to \((x - 4)(x + 6)=0\).

Step3: Solve for \(x\)

Set each factor equal to zero: \(x - 4 = 0\) or \(x + 6 = 0\). Solving these gives \(x = 4\) or \(x = -6\).

Answer:

\(x = 4\) or \(x = -6\)