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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]?

A. [tex]5(x - 1) - x^2 - 1[/tex]
B. [tex](5x - 1) - (x^2 - 1)[/tex]
C. [tex](x^2 - 1) - 5(x - 1)[/tex]
D. [tex](x^2 - 1) - 5x - 1[/tex]

Sagot :

GinnyAnsweridn
To find the expression equivalent to [tex]\((p - q)(x)\)[/tex], we need to calculate [tex]\(p(x) - q(x)\)[/tex].

First, let's rewrite the given functions for clarity:
[tex]\[ p(x) = x^2 - 1 \][/tex]
[tex]\[ q(x) = 5(x - 1) \][/tex]

Now, we will calculate [tex]\(p(x) - q(x)\)[/tex]:
[tex]\[ (p - q)(x) = p(x) - q(x) \][/tex]

Substitute the functions [tex]\(p(x)\)[/tex] and [tex]\(q(x)\)[/tex]:
[tex]\[ (p - q)(x) = (x^2 - 1) - 5(x - 1) \][/tex]

Next, simplify the expression:
[tex]\[ (p - q)(x) = (x^2 - 1) - 5x + 5 \][/tex]

Combining like terms, we get:
[tex]\[ (p - q)(x) = x^2 - 1 - 5x + 5 \][/tex]
[tex]\[ (p - q)(x) = x^2 - 5x - 1 + 5 \][/tex]
[tex]\[ (p - q)(x) = x^2 - 5x + 4 \][/tex]

Therefore, the correct expression equivalent to [tex]\((p - q)(x)\)[/tex] is:
[tex]\[ \left(x^2 - 1\right) - 5(x - 1) \][/tex]

This matches the third option in the list provided:
[tex]\[ \left(x^2 - 1\right) - 5(x - 1) \][/tex]
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