Question

In the following exercises, factor each trinomial of the form $x^2+bx+c$

$7x+x^2+6$

Short answer

The factorization of$7x+x^2+6$is$(x+6)(x+1)$

Step-by-step solution

Step 1. Given information

Given expression is$7x+x^2+6$

Step 2. Find the last terms of the binomial.

The factor of the expression:

The factor of 6	Sum of factor
2, 3	2 + 3 = 5
6, 1	6 + 1 = 7

Step 3. Factorization

Use $6$and $1$as the terms of the binomial.

$7x+x^2+6x=(x+6)(x+1)$

Step 4. Check

$$\begin{gathered} (x+6)(x+1)=x^2+6x+x+6 \\ =x^2+7x+6 \\ =7x+x^2+6 \end{gathered}$$