To factor the quadratic expression \(x^2 + 6x - 16\), we can attempt to factor it into the form \((x + a)(x + b)\), where \(a\) and \(b\) are two numbers whose product is equal to the constant term \(-16\) and whose sum is equal to the coefficient of the linear term, which is \(6\).

Let's break it down:

1. We need two numbers that multiply to \(-16\) and add up to \(6\).
   - The two numbers are \(8\) and \(-2\), since:
     - \(8 \times (-2) = -16\)
     - \(8 + (-2) = 6\)

Thus, the factorization is:

\[
x^2 + 6x - 16 = (x + 8)(x - 2)
\]

Would you like further details on this, or do you have any other questions?

Here are 5 related questions:
1. How can you verify that \((x + 8)(x - 2)\) is the correct factorization?
2. What is the solution to the equation \(x^2 + 6x - 16 = 0\)?
3. Can every quadratic expression be factored in this way?
4. What is the relationship between the factors and the roots of a quadratic equation?
5. How would the factorization change if the quadratic expression had a different constant term?

**Tip:** If you can't factor a quadratic directly, consider using the quadratic formula for a general solution.

Learn how to factor the quadratic expression x² + 6x - 16 by identifying two numbers that multiply to -16 and add to 6. This detailed solution breaks down the steps to solve it, making it suitable for students in Grades 8-10.

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