https://file.aiquickdraw.com/mathbot/file/1729563781524oocqhx3m.jpg

The expression provided is:

\[
6x^2 + 24x - 72
\]

This is a quadratic expression, and it can be simplified by factoring. First, we can factor out the greatest common factor (GCF) from all the terms.

### Step 1: Factor out the GCF
The GCF of \(6x^2\), \(24x\), and \(-72\) is 6.

\[
6(x^2 + 4x - 12)
\]

### Step 2: Factor the quadratic expression \(x^2 + 4x - 12\)
We need to factor the quadratic expression inside the parentheses, but since it doesn't factor nicely, we can solve it using the quadratic formula.

The quadratic formula is:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the equation \(x^2 + 4x - 12 = 0\), we have:
- \(a = 1\)
- \(b = 4\)
- \(c = -12\)

### Step 3: Apply the quadratic formula
Substitute the values into the formula:
\[
x = \frac{-4 \pm \sqrt{4^2 - 4(1)(-12)}}{2(1)}
\]
\[
x = \frac{-4 \pm \sqrt{16 + 48}}{2}
\]
\[
x = \frac{-4 \pm \sqrt{64}}{2}
\]
\[
x = \frac{-4 \pm 8}{2}
\]

### Step 4: Find the solutions
Now, we calculate both possible values of \(x\):
1. \(x = \frac{-4 + 8}{2} = \frac{4}{2} = 2\)
2. \(x = \frac{-4 - 8}{2} = \frac{-12}{2} = -6\)

Thus, the factored form is:
\[
6(x - 2)(x + 6)
\]

### Final Factored Form:
\[
6(x - 2)(x + 6)
\]

Let me know if you'd like more details or have any questions!

Here are some related questions:
1. What are the roots of the equation \(6x^2 + 24x - 72 = 0\)?
2. How does the quadratic formula help in solving non-factorable quadratic equations?
3. What does factoring a quadratic equation tell you about its graph?
4. Can all quadratic expressions be factored without using the quadratic formula?
5. How would you solve this quadratic equation graphically?

**Tip:** Factoring a quadratic equation when possible can give you the roots easily and reveal important characteristics of the function's graph (such as intercepts).

Simplify and factor the quadratic expression: 6x^2 + 24x - 72

This page explains how to factor the quadratic expression 6x^2 + 24x - 72 by finding the greatest common factor (GCF) and applying the quadratic formula. Follow a detailed step-by-step solution suitable for students in Grades 9-11.

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