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The problem asks to **factor the quadratic expression** \(x^2 - 14x + 40\).

### Step-by-Step Solution:
1. **Look for two numbers** that multiply to \(40\) (the constant term) and add to \(-14\) (the coefficient of the middle term, \(x\)).

2. These two numbers are \(-4\) and \(-10\), since:
   - \(-4 \times -10 = 40\)
   - \(-4 + -10 = -14\)

3. Now, write the quadratic as:
   \[
   x^2 - 14x + 40 = (x - 4)(x - 10)
   \]

Thus, the factored form of \(x^2 - 14x + 40\) is:
\[
(x - 4)(x - 10)
\]

Would you like further clarification on any part of this solution? 

Here are five related questions you could explore:
1. How do you factor trinomials when the leading coefficient \(a \neq 1\)?
2. What is the connection between factoring and solving quadratic equations?
3. How can factoring help in finding the roots of a quadratic equation?
4. What happens if a quadratic cannot be factored easily by integers?
5. Can you explain the difference between completing the square and factoring?

**Tip:** Always check your factorization by multiplying the factors back together to ensure they match the original expression!

Factor the quadratic expression x^2 - 14x + 40.

This page explains how to factor the quadratic expression x^2 - 14x + 40 using algebraic techniques. It covers core concepts in factoring trinomials and is suitable for students in grades 8-10.

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