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We are asked to factor the quadratic expression \( 2x^2 - 11x + 9 \). The general form of factoring is \( (2x + m)(x + n) \), where we need to determine the correct signs and values for \( m \) and \( n \).

### Steps to factor:
1. Multiply the leading coefficient (2) by the constant term (9), which gives \( 2 \times 9 = 18 \).
2. Now, we need two numbers that multiply to 18 and add up to the middle coefficient, which is -11.

The two numbers that satisfy this are -9 and -2, because:
\[
-9 \times -2 = 18 \quad \text{and} \quad -9 + -2 = -11.
\]

3. Now, we split the middle term:
\[
2x^2 - 9x - 2x + 9.
\]
4. Factor by grouping:
\[
x(2x - 9) - 1(2x - 9) = (x - 1)(2x - 9).
\]

Thus, the factorization is \( (2x - 9)(x - 1) \).

### Answer:
The correct symbols are:
- \( 2x - 9 \)
- \( x - 1 \).

Would you like more details on factoring techniques, or do you have further questions?

Here are 5 related questions:
1. What is the general form of factoring quadratic expressions?
2. How can you identify the right pair of factors for the middle term?
3. Why is grouping an effective method for factoring quadratics?
4. How can you check if a factored form is correct?
5. What is the role of the leading coefficient in factoring?

**Tip**: Always multiply the factors back together to verify your result!

Factor the quadratic expression 2x^2 - 11x + 9.

This page explains how to factor the quadratic expression 2x^2 - 11x + 9 using factoring by grouping. Learn the detailed steps and understand the logic behind this method, suitable for students in Grades 9-11.

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