If p(x)=x^2-1 and q(x)-5(x-1) which expression is equivalent to (p-q)(x) 7 5(x-1)-x^2-1 (5x-1)-(x^2-1) (x^2-1)-5(x-1) (x^2-1)-5x-1

To find the expression equivalent to \((p - q)(x)\), we need to subtract \(q(x)\) from \(p(x)\).<br /><br />Given:<br />\[ p(x) = x^2 - 1 \]<br />\[ q(x) = 5(x - 1) \]<br /><br />First, let's simplify \(q(x)\):<br />\[ q(x) = 5(x - 1) = 5x - 5 \]<br /><br />Now, we can find \((p - q)(x)\):<br />\[ (p - q)(x) = p(x) - q(x) \]<br />\[ (p - q)(x) = (x^2 - 1) - (5x - 5) \]<br /><br />Distribute the negative sign:<br />\[ (p - q)(x) = x^2 - 1 - 5x + 5 \]<br /><br />Combine like terms:<br />\[ (p - q)(x) = x^2 - 5x + 4 \]<br /><br />So, the expression equivalent to \((p - q)(x)\) is:<br />\[ (x^2 - 1) - 5(x - 1) \]<br /><br />Therefore, the correct answer is:<br />\[ (x^2 - 1) - 5(x - 1) \]