Question

Follow these steps to factor x^2+13x+12
Use this as reference: x^2+bx+c=(x+p)(x+q)

Answer 1

To factor the quadratic expression \(x^2 + 13x + 12\) using the form \(x^2 + bx + c = (x + p)(x + q)\), follow these steps:

1. **Identify coefficients**: In the expression \(x^2 + 13x + 12\), we have:
- \(b = 13\)
- \(c = 12\)

2. **Find \(p\) and \(q\)**: We need to find two numbers \(p\) and \(q\) such that:
- \(p + q = b = 13\)
- \(p \cdot q = c = 12\)

3. **List the factor pairs of 12**: The possible pairs that multiply to 12 are:
- \(1 \cdot 12\)
- \(2 \cdot 6\)
- \(3 \cdot 4\)

4. **Determine the correct pair**: We need to find which pair adds up to 13:
- For \(1\) and \(12\): \(1 + 12 = 13\) (this works!)
- For \(2\) and \(6\): \(2 + 6 = 8\) (not a match)
- For \(3\) and \(4\): \(3 + 4 = 7\) (not a match)

The only suitable pair is \(p = 1\) and \(q = 12\).

5. **Write the factored form**: Now we can express \(x^2 + 13x + 12\) as:
\[
(x + 1)(x + 12)
\]

So, the factored form of \(x^2 + 13x + 12\) is \((x + 1)(x + 12)\).