Factor.

x, squared, plus, 7, x, plus, 12

*x*2+7*x*+12

To factor the expression \(x^2 + 7x + 12\), we look for two numbers that multiply to \(12\) (the constant term) and add up to \(7\) (the coefficient of \(x\)).

### Step 1: Find Two Numbers That Multiply to \(12\) and Add to \(7\)
The two numbers that satisfy these conditions are \(3\) and \(4\) because:
\[
3 \cdot 4 = 12 \quad \text{and} \quad 3 + 4 = 7
\]

### Step 2: Write the Expression as a Product of Two Binomials
Using these numbers, we can factor the expression as:
\[
x^2 + 7x + 12 = (x + 3)(x + 4)
\]

### Final Answer
The factored form of the expression is:

\[
(x + 3)(x + 4)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you factor \(x^2 + 8x + 15\)?
2. What are the steps for factoring \(x^2 + 6x + 9\)?
3. How can you check if your factorization is correct?
4. What happens if the middle term coefficient is negative, like in \(x^2 - 7x + 12\)?
5. How would you factor \(x^2 + 5x + 6\)?

**Tip**: When factoring trinomials, look for two numbers that multiply to the constant term and add up to the middle term's coefficient.

Discover how to factor the quadratic expression x^2 + 7x + 12 with a clear step-by-step solution. Learn algebraic techniques for factoring trinomials, understanding key mathematical concepts and formulas. Perfect for students in Grades 8-10.

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