The expression you provided seems to represent a quadratic polynomial:

\[
2x^2 + 9x + 10
\]

To work with this expression, we can explore several operations, like factoring, solving for roots, or evaluating it for specific values of \( x \). I'll go through the factoring process.

### Factoring \( 2x^2 + 9x + 10 \)

To factor this expression, we look for two numbers that multiply to \( 2 \times 10 = 20 \) and add up to \( 9 \). These numbers are \( 5 \) and \( 4 \).

1. Rewrite the middle term \( 9x \) as \( 5x + 4x \):
   \[
   2x^2 + 5x + 4x + 10
   \]

2. Factor by grouping:
   \[
   = x(2x + 5) + 2(2x + 5)
   \]

3. Factor out \( (2x + 5) \):
   \[
   = (2x + 5)(x + 2)
   \]

Thus, the factored form of \( 2x^2 + 9x + 10 \) is:
\[
(2x + 5)(x + 2)
\]

Let me know if you'd like further details or have any questions about this process!

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**Related Questions:**

1. How do you solve for \( x \) when a quadratic is set to zero?
2. What methods can you use if factoring isn’t immediately apparent?
3. What is the quadratic formula, and how does it apply here?
4. How would you complete the square for the expression \( 2x^2 + 9x + 10 \)?
5. Can we graph the polynomial, and what would its roots represent?

**Tip:** For any quadratic expression \( ax^2 + bx + c \), check if factoring is possible by examining possible pairs of factors for \( a \times c \) that add to \( b \).

Learn how to factor the quadratic polynomial 2x^2 + 9x + 10 using a step-by-step approach. This guide covers key algebraic concepts, factoring techniques, and essential methods suitable for students in Grades 8-10.

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