16. ((x^4 + 4x^3 + 16x - 35) div (x + 5))

Explanation:

Step1: Set up polynomial long division

Divide $x^4 + 4x^3 + 0x^2 + 16x - 35$ by $x+5$ (added $0x^2$ for missing term)

Step2: Divide leading terms

$\frac{x^4}{x} = x^3$. Multiply divisor by $x^3$: $x^3(x+5)=x^4+5x^3$. Subtract from dividend: $(x^4 + 4x^3) - (x^4 + 5x^3) = -x^3$ Bring down next term: $-x^3 + 0x^2$

Step3: Divide leading terms again

$\frac{-x^3}{x} = -x^2$. Multiply divisor by $-x^2$: $-x^2(x+5)=-x^3-5x^2$. Subtract: $(-x^3 + 0x^2) - (-x^3 - 5x^2) = 5x^2$ Bring down next term: $5x^2 + 16x$

Step4: Divide leading terms

$\frac{5x^2}{x} = 5x$. Multiply divisor by $5x$: $5x(x+5)=5x^2+25x$. Subtract: $(5x^2 + 16x) - (5x^2 + 25x) = -9x$ Bring down last term: $-9x - 35$

Step5: Divide leading terms

$\frac{-9x}{x} = -9$. Multiply divisor by $-9$: $-9(x+5)=-9x-45$. Subtract: $(-9x - 35) - (-9x - 45) = 10$

Answer:

Quotient: $x^3 - x^2 + 5x - 9$, Remainder: $10$ Or written as: $x^3 - x^2 + 5x - 9 + \frac{10}{x+5}$