Question

1. ((x^{3}+6x^{2}+11x + 6)div(x + 1))

Explanation:

Step1: Use polynomial long division

Set up division: divide $x^3+6x^2+11x+6$ by $x+1$.
First term: $\frac{x^3}{x}=x^2$. Multiply divisor: $x^2(x+1)=x^3+x^2$. Subtract:
$(x^3+6x^2+11x+6)-(x^3+x^2)=5x^2+11x+6$

Step2: Divide next leading term

$\frac{5x^2}{x}=5x$. Multiply divisor: $5x(x+1)=5x^2+5x$. Subtract:
$(5x^2+11x+6)-(5x^2+5x)=6x+6$

Step3: Divide final leading term

$\frac{6x}{x}=6$. Multiply divisor: $6(x+1)=6x+6$. Subtract:
$(6x+6)-(6x+6)=0$

Answer:

$x^2 + 5x + 6$