Answer:
(x+4)(x-6)
Explanation:
Given the trinomial:
[tex]x^2-2x-24[/tex]Factoring means we want an expression of the form: (x+_)(x+_).
To find the two numbers, we need two terms:
• Whose sum is the middle term, -2x
,• Whose product is: -24x²
[tex]\begin{gathered} -6x+4x=-2x \\ (-6x)(4x)=-24x^2 \end{gathered}[/tex]Replace the middle term with the sum.
[tex]x^2-2x-24=x^2-6x+4x-24[/tex]Next, group into two and factor it, ensuring that the expression inside the brackets is the same.
[tex]\begin{gathered} =x(x-6)+4(x-6) \\ =(x+4)(x-6) \end{gathered}[/tex]The factored form of the trinomial is (x+4)(x-6).
