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The image presents a problem focused on factoring a quadratic equation. Here’s the breakdown of the solution:

Given:
\[
y = x^2 + 2x - 8
\]

To factor this equation, we need to find two numbers that multiply to \(-8\) (the constant term) and add up to \(2\) (the coefficient of \(x\)).

The numbers that satisfy these conditions are \(4\) and \(-2\), because:
\[
4 \times -2 = -8 \quad \text{and} \quad 4 + (-2) = 2
\]

Thus, we can factor the equation as:
\[
y = (x - 2)(x + 4)
\]

So, the factored form of the equation is:
\[
y = (x - 2)(x + 4)
\]

Would you like more details, or do you have any questions?

### Related Questions
1. How would you factor a quadratic expression if the coefficient of \(x^2\) was greater than 1?
2. What are some techniques for quickly identifying factor pairs of a constant term?
3. How would you handle a quadratic expression that cannot be factored into real numbers?
4. Can this factoring method be applied to quadratic equations with complex roots?
5. How does factoring relate to finding the roots of a quadratic equation?

### Tip
Always check your factors by expanding them to ensure they match the original expression. This helps confirm accuracy.

Factoring is an algebraic process, which is an essential one in the field of mathematics. Consider the following equation: y = x^2 + 2x - 8. This equation in factored form can be written as: y = (x - 2)(x + 4).

Learn how to factor the quadratic equation y = x^2 + 2x - 8 step-by-step. This guide covers the essential algebraic process of factoring, finding values that multiply to the constant term and add to the coefficient of x. Perfect for students in Grades 8-10.

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