Question

Organizing Information
Follow these steps to factor x+ 13x + 12.
Use this as reference: x'+ bx + c= (x+p)(x+q)
Step 1: Identify c in the trinomial.
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Step 2: Find all the possible factor pairs (poq) for c.
(Table to the right)
List each pair as p and q in one row of this table.
(Remember to account for negative signs!)
Step 3: Find the sum of each factor pair (p+q). (Table to the right)
List the sum in the correct row of the table.
Step 4: Identify b in the trinomial.
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Step 5: Find the factor pair that has the sum b.
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Answer 1

Let’s go through the steps to factor the trinomial \(x^2 + 13x + 12\).

### Step 1: Identify \(c\) in the trinomial.
In the trinomial \(x^2 + bx + c\), \(c\) is the constant term.
- **Answer**:
\[
c = 12
\]

### Step 2: Find all the possible factor pairs (poq) for \(c\).
Possible pairs of integers (p, q) that multiply to give \(c = 12\) are:
- (1, 12)
- (2, 6)
- (3, 4)

Now let's create the table.

| p | q |
|---|---|
| 1 | 12 |
| 2 | 6 |
| 3 | 4 |

### Step 3: Find the sum of each factor pair (p + q).
Now, we will calculate the sum of each factor pair.

| p | q | p + q |
|---|---|-------|
| 1 | 12 | 13 |
| 2 | 6 | 8 |
| 3 | 4 | 7 |

### Step 4: Identify \(b\) in the trinomial.
In the trinomial \(x^2 + bx + c\), \(b\) is the coefficient of \(x\).
- **Answer**:
\[
b = 13
\]

### Step 5: Find the factor pair that has the sum \(b\).
We are looking for the factor pair (p, q) whose sum \(p + q = b = 13\).
From the table, we see:
- The pair (1, 12) has the sum \(1 + 12 = 13\).

Thus,
- **Answer**:
\[
p = 1
\]
\[
q = 12
\]

### Final Factored Form
The factored form of the trinomial \(x^2 + 13x + 12\) is:
\[
(x + 1)(x + 12)
\]