https://file.aiquickdraw.com/mathbot/file/172709166267956d7k3tv.jpg

The equation visible in the image is:

\[
4x^2 + 9x + 2
\]

This is a quadratic expression, and we can factor or solve it depending on the goal. Let me walk you through factoring it first.

### To factor the quadratic:
We are looking for two numbers that multiply to \(4 \times 2 = 8\) and add up to \(9\). These two numbers are \(8\) and \(1\).

Thus, we can rewrite the quadratic as:
\[
4x^2 + 8x + x + 2
\]
Now, factor by grouping:
\[
(4x^2 + 8x) + (x + 2) = 4x(x + 2) + 1(x + 2)
\]
Factor out the common binomial:
\[
(4x + 1)(x + 2)
\]

So, the factored form of the quadratic expression is:
\[
(4x + 1)(x + 2)
\]

Would you like further details or any clarifications?

Here are some related questions:
1. How do we solve a quadratic equation using the quadratic formula?
2. What are the key differences between factoring and using the quadratic formula?
3. How can we determine the nature of the roots of a quadratic equation?
4. How does completing the square work for solving quadratics?
5. Can every quadratic equation be factored easily?

**Tip:** Always try factoring simpler expressions first, but if it becomes difficult, the quadratic formula is a reliable fallback!

Factor the quadratic equation 4x^2 + 9x + 2.

Learn how to factor the quadratic equation 4x^2 + 9x + 2 using factoring by grouping. This detailed guide walks you through the process of breaking down the quadratic expression and factoring it step by step. Suitable for students in Grades 9-10.

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