Question

divide. if the polynomial does not divide evenly, include the remainder as a fraction.
\\((-x^2 + 24) \div (x - 5)\\)

Explanation:

Step1: Set up polynomial long division

Divide $-x^2 + 0x + 24$ by $x-5$ (add $0x$ for missing term)

Step2: Divide leading terms

$\frac{-x^2}{x} = -x$
Multiply divisor by $-x$: $-x(x-5) = -x^2 + 5x$
Subtract from dividend:
$(-x^2 + 0x + 24) - (-x^2 + 5x) = -5x + 24$

Step3: Divide new leading terms

$\frac{-5x}{x} = -5$
Multiply divisor by $-5$: $-5(x-5) = -5x + 25$
Subtract from current remainder:
$(-5x + 24) - (-5x + 25) = -1$

Step4: Write final result

Quotient plus remainder over divisor

Answer:

$-x - 5 - \frac{1}{x-5}$