Simplify (x^3-x^2-5x-3)÷(x^2+2x+1)

$(x^{3} - x^{2} - 5 x - 3) \div (x^{2} + 2 x + 1)$

Rewrite the division as a fraction.

$\frac{x^{3} - x^{2} - 5 x - 3}{x^{2} + 2 x + 1}$

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$\frac{x^{3} - x^{2} - 5 x - 3}{x^{2} + 2 x + 1^{2}}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x = 2 \cdot x \cdot 1$

Rewrite the polynomial.

$\frac{x^{3} - x^{2} - 5 x - 3}{x^{2} + 2 \cdot x \cdot 1 + 1^{2}}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 1$ .

$\frac{x^{3} - x^{2} - 5 x - 3}{{(x + 1)}^{2}}$