Question

Factor completely:

$x^2+13x+36$.

Short answer

The factored polynomial is,

$(x+9)(x+4)$.

Step-by-step solution

Step 1. Given the information.

The polynomial is,

$x^2+13x+36$.

Step 2. Factoring the polynomial.

$x^2+13x+36$

Splitting the middle term such that the sum of the terms is $13$and the product of the terms is $36$.

$=x^2+9x+4x+36$

$=(x^2+9x)+(4x+36)$

Taking out the common factors,

$$\begin{gathered} =x(x+9)+4(x+9) \\ =(x+9)(x+4) \end{gathered}$$

Step 3. Checking the solution.

$(x+9)(x+4)$

Multiplying the brackets,

$$\begin{gathered} =x(x+4)+9(x+4) \\ =x^2+4x+9x+36 \\ =x^2+13x+36 \end{gathered}$$

This is true.