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The given expression to factor by grouping is:

\[
x^3 + 4x^2 - 9x - 36
\]

We will attempt to group terms and factor the expression.

### Step 1: Group the terms
Group the terms in pairs:

\[
(x^3 + 4x^2) - (9x + 36)
\]

### Step 2: Factor out the greatest common factor (GCF) from each group
For the first group \(x^3 + 4x^2\), the GCF is \(x^2\):

\[
x^2(x + 4)
\]

For the second group \(-9x - 36\), the GCF is \(-9\):

\[
-9(x + 4)
\]

### Step 3: Factor the common binomial
Now the expression looks like this:

\[
x^2(x + 4) - 9(x + 4)
\]

Since both terms contain \((x + 4)\), we can factor that out:

\[
(x + 4)(x^2 - 9)
\]

### Step 4: Factor the difference of squares
The expression \(x^2 - 9\) is a difference of squares, which can be factored as:

\[
x^2 - 9 = (x - 3)(x + 3)
\]

### Final factored form:
\[
(x + 4)(x - 3)(x + 3)
\]

The factored form of the given expression is:

\[
(x + 4)(x - 3)(x + 3)
\]

Would you like any further details or have any questions?

Here are some related questions:
1. What is the difference of squares rule?
2. How do you identify common factors in algebraic expressions?
3. Can you factor a cubic equation directly without grouping?
4. How does factoring help in solving polynomial equations?
5. What are other methods for factoring polynomials?

**Tip:** Always check for common factors before applying advanced factoring methods, as this simplifies the expression early on.

Learn how to factor the cubic polynomial x^3 + 4x^2 - 9x - 36 using the method of grouping. Follow a step-by-step guide that includes factoring by grouping, recognizing common binomials, and using the difference of squares formula. This problem is suitable for Grades 9-11.

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