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If [tex]\( p(x) = x^2 - 1 \)[/tex] and [tex]\( q(x) = 5(x - 1) \)[/tex], which expression is equivalent to [tex]\( (p - q)(x) \)[/tex]?
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].
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.
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