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The given expression is \( x^2 + 7x + 10 \), and you are asked to factor it.

To factor this quadratic expression, we need to find two numbers that:
1. Multiply to give the constant term (10).
2. Add to give the coefficient of the middle term (7).

The two numbers that work are 5 and 2, because:
- \( 5 \times 2 = 10 \)
- \( 5 + 2 = 7 \)

Thus, the factored form of the expression is:
\[
x^2 + 7x + 10 = (x + 5)(x + 2)
\]

Would you like further explanation or any additional help with this problem?

Here are five related questions to explore this topic further:
1. How can you factor quadratics where the leading coefficient is not 1?
2. What is the process of factoring perfect square trinomials?
3. How do you factor quadratic expressions using the quadratic formula?
4. Can you always factor quadratic expressions by grouping?
5. How do you factor trinomials where the constant is negative?

**Tip**: Always check your factors by multiplying them back together to ensure they give you the original quadratic expression.

Learn how to factor the quadratic equation x^2 + 7x + 10 with a clear step-by-step solution. This problem covers key algebraic concepts, including how to find two numbers that multiply to the constant term and add up to the middle coefficient. Ideal for students in Grades 7-9.

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