Simplify (x^3+10x^2+13x+39)/(x^2+2x+1)

$\frac{x^{3} + 10 x^{2} + 13 x + 39}{x^{2} + 2 x + 1}$

Step 1

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

$\frac{x^{3} + 10 x^{2} + 13 x + 39}{x^{2} + 2 x + 1^{2}}$

Step 2

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

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

Step 3

Rewrite the polynomial.

$\frac{x^{3} + 10 x^{2} + 13 x + 39}{x^{2} + 2 \cdot x \cdot 1 + 1^{2}}$

Step 4

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

$\frac{x^{3} + 10 x^{2} + 13 x + 39}{{(x + 1)}^{2}}$