To solve the problem of identifying the missing factor in the binomial expression [tex]\(x^2 - 49\)[/tex], we start by recognizing the form of the expression. The expression [tex]\(x^2 - 49\)[/tex] represents a difference of squares and can be factored using the difference of squares formula.
The difference of squares formula is:
[tex]\[
a^2 - b^2 = (a + b)(a - b)
\][/tex]
In our given expression, [tex]\(x^2 - 49\)[/tex], we can identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] as follows:
[tex]\[
a^2 = x^2 \quad \text{and} \quad b^2 = 49
\][/tex]
So, [tex]\(a = x\)[/tex] and [tex]\(b = 7\)[/tex].
Using these values in the difference of squares formula, we factorize [tex]\(x^2 - 49\)[/tex] as:
[tex]\[
x^2 - 49 = (x + 7)(x - 7)
\][/tex]
We see that the correct factorization of [tex]\(x^2 - 49\)[/tex] splits it into two binomials: [tex]\((x + 7)\)[/tex] and [tex]\((x - 7)\)[/tex].
Given that the expression [tex]\(x^2 - 49\)[/tex] has been partially factored into:
[tex]\[
x^2 - 49 = (x + 7)
\][/tex]
we can now identify the missing factor needed to complete the factorization, which is:
[tex]\[
(x - 7)
\][/tex]
Therefore, the missing factor is:
[tex]\[
\boxed{(x - 7)}
\][/tex]
