Question

1. ((x^2 + 9) div (x + 4))

Explanation:

Step1: Set up polynomial long division

Divide $x^2 + 0x + 9$ by $x + 4$ (adding $0x$ for clarity)

Step2: Divide leading terms

$\frac{x^2}{x} = x$. Multiply divisor by $x$:
$x(x + 4) = x^2 + 4x$

Step3: Subtract from dividend

$(x^2 + 0x + 9) - (x^2 + 4x) = -4x + 9$

Step4: Divide new leading terms

$\frac{-4x}{x} = -4$. Multiply divisor by $-4$:
$-4(x + 4) = -4x - 16$

Step5: Subtract to find remainder

$(-4x + 9) - (-4x - 16) = 25$

Answer:

$x - 4 + \frac{25}{x + 4}$