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We are tasked with factoring the quadratic expression \(x^2 - 10x + 9\).

### Step-by-Step Solution:

We are looking to factor this trinomial into two binomials of the form:
\[
(x - m)(x - n)
\]
where \(m\) and \(n\) are two numbers that:
1. Multiply to give the constant term (here, \(9\)).
2. Add to give the middle coefficient (here, \(-10\)).

So, we need two numbers that multiply to \(9\) and add up to \(-10\). The numbers are \(-1\) and \(-9\), since:
\[
-1 \times -9 = 9 \quad \text{and} \quad -1 + (-9) = -10
\]

Thus, the factorization of \(x^2 - 10x + 9\) is:
\[
(x - 1)(x - 9)
\]

This is the factored form of the quadratic expression.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. How would you factor a trinomial where the coefficient of \(x^2\) (the "a" value) is greater than 1?
2. What is the relationship between factoring and solving quadratic equations?
3. Can all quadratic expressions be factored using real numbers? Why or why not?
4. How do you verify that your factorization is correct?
5. What does the factored form tell us about the roots of the quadratic equation?

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

Factor the quadratic equation: x^2 - 10x + 9

Learn how to factor the quadratic expression x^2 - 10x + 9 into (x - 1)(x - 9). This problem involves factoring trinomials and understanding algebraic concepts. Suitable for students in Grades 7-9.

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