https://file.aiquickdraw.com/mathbot/file/1726111782532tnan84w5.jpg

The text extraction from the image did not succeed, but I can clearly read the equation \( x^2 + x - 30 \) from the image you provided. Let's factor this quadratic equation.

We are factoring \( x^2 + x - 30 \).

To do this, we look for two numbers that multiply to give \(-30\) (the constant term) and add to give \(1\) (the coefficient of \(x\)).

The numbers are \(6\) and \(-5\), because:

\[
6 \times -5 = -30 \quad \text{and} \quad 6 + (-5) = 1.
\]

So, we can factor the equation as:

\[
x^2 + x - 30 = (x + 6)(x - 5).
\]

Thus, the factored form is:

\[
(x + 6)(x - 5).
\]

Would you like more details on this or have any questions?

Here are some related questions:
1. How do you factor quadratic equations in general?
2. What are the applications of factoring in solving quadratic equations?
3. Can you always factor quadratic equations using integers?
4. What are other methods to solve quadratic equations apart from factoring?
5. How can we confirm if our factoring is correct?

**Tip:** When factoring quadratic equations, it's helpful to always check by expanding the factors to verify if you get back the original expression.

Factor the quadratic equation x^2 + x - 30.

This article provides a step-by-step guide to factoring the quadratic equation x^2 + x - 30. Learn how to find factors that multiply to -30 and add to 1 to solve this equation, suitable for students in Grades 8-10.

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