To find which expression is equivalent to [tex]\((p - q)(x)\)[/tex], we first need to express it in terms of [tex]\(p(x)\)[/tex] and [tex]\(q(x)\)[/tex].
Given:
[tex]\[ p(x) = x^2 - 1 \][/tex]
[tex]\[ q(x) = 5(x - 1) \][/tex]
We need to find [tex]\((p - q)(x)\)[/tex], which means we subtract [tex]\(q(x)\)[/tex] from [tex]\(p(x)\)[/tex]:
[tex]\[ (p - q)(x) = p(x) - q(x) \][/tex]
Now, substitute the expressions for [tex]\(p(x)\)[/tex] and [tex]\(q(x)\)[/tex]:
[tex]\[ (p - q)(x) = (x^2 - 1) - 5(x - 1) \][/tex]
This is the expression we need to simplify, but let's first verify if it matches one of the given options.
The given options are:
1. [tex]\(5(x - 1) - x^2 - 1\)[/tex]
2. [tex]\( (5x - 1) - (x^2 - 1)\)[/tex]
3. [tex]\( (x^2 - 1) - 5(x - 1) \)[/tex]
4. [tex]\( (x^2 - 1) - 5x - 1 \)[/tex]
Looking closely at the expressions, the correct matching expression is:
[tex]\[ (x^2 - 1) - 5(x - 1) \][/tex]
Which is option 3.
Therefore, the answer is option 3.
