Question

factor ( k^2 - 10k + 24 ). the factored expression is \\(\square\\).

Explanation:

Step1: Find two numbers that multiply to 24 and add to -10.

We need two numbers \(a\) and \(b\) such that \(a \times b = 24\) and \(a + b = -10\). The numbers are -6 and -4 because \((-6)\times(-4)=24\) and \((-6)+(-4)=-10\).

Step2: Factor the quadratic using these numbers.

The quadratic \(k^{2}-10k + 24\) can be factored as \((k - 6)(k - 4)\) since \((k - 6)(k - 4)=k^{2}-4k-6k + 24=k^{2}-10k + 24\).

Answer:

\((k - 6)(k - 4)\)