To factor the quadratic expression \( x^2 + 6x - 16 \), we can use the factoring technique known as **splitting the middle term**. Here's the process:

1. **Identify the quadratic form**: The given expression is in the form \( ax^2 + bx + c \), where \( a = 1 \), \( b = 6 \), and \( c = -16 \).

2. **Find two numbers** that multiply to give \( a \times c = 1 \times (-16) = -16 \), and add up to give \( b = 6 \).

   - The two numbers that satisfy this condition are **8** and **-2** because:
     \[
     8 \times (-2) = -16 \quad \text{and} \quad 8 + (-2) = 6
     \]

3. **Rewrite the middle term** using these two numbers**:
   \[
   x^2 + 8x - 2x - 16
   \]

4. **Factor by grouping**:
   \[
   (x^2 + 8x) - (2x + 16)
   \]
   Factor out the greatest common factor from each group:
   \[
   x(x + 8) - 2(x + 8)
   \]

5. **Factor out the common binomial**:
   \[
   (x - 2)(x + 8)
   \]

So, the factorized form of \( x^2 + 6x - 16 \) is:
\[
(x - 2)(x + 8)
\]

Would you like further explanation on any step?

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Here are 5 related questions:
1. How would you factor a quadratic with a leading coefficient other than 1?
2. Can every quadratic equation be factored into binomials?
3. What is the difference between factoring and solving a quadratic equation?
4. How would you apply the quadratic formula to solve \(x^2 + 6x - 16 = 0\)?
5. How can completing the square be used as an alternative method to factor \(x^2 + 6x - 16\)?

**Tip**: When factoring quadratics, always check if you can simplify the middle term by finding two numbers that fit both the product and sum conditions.

Learn how to factor the quadratic equation x² + 6x - 16 using the method of splitting the middle term. This step-by-step guide walks through factoring by grouping and covers key algebraic concepts. Perfect for students in Grades 8-10.

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