Question

factor the following trinomial.\\(x^2 - 2x - 48\\)\\((x - ?)(x + \quad)\\)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-48\) and add up to \(-2\). Let's list the factor pairs of \(-48\): \((-8, 6)\) because \(-8\times6 = -48\) and \(-8 + 6=-2\).

Step2: Factor the trinomial

Using the numbers \(-8\) and \(6\), we can factor \(x^{2}-2x - 48\) as \((x - 8)(x + 6)\) since when we multiply \((x - 8)(x + 6)\), we get \(x^{2}+6x-8x - 48=x^{2}-2x - 48\).

Answer:

The first blank (green) is \(8\) and the second blank (gray) is \(6\), so the factored form is \((x - 8)(x + 6)\).