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The given expression is:

\[
3x^{56} - 15x^{58} + 12x^{60}
\]

We can factor this expression by looking for the greatest common factor (GCF) among the terms.

### Step 1: Find the GCF
The coefficients of the terms are \(3\), \(-15\), and \(12\). The GCF of these numbers is \(3\).

The powers of \(x\) in the terms are \(x^{56}\), \(x^{58}\), and \(x^{60}\). The lowest power is \(x^{56}\), so the GCF of the powers of \(x\) is \(x^{56}\).

Thus, the overall GCF is \(3x^{56}\).

### Step 2: Factor the expression
We factor out \(3x^{56}\) from each term:

\[
3x^{56}(1 - 5x^2 + 4x^4)
\]

So the factored form of the expression is:

\[
3x^{56}(1 - 5x^2 + 4x^4)
\]

Would you like a detailed explanation of any specific step, or have any questions? 

Here are 5 related questions to expand on this:

1. How do you find the greatest common factor (GCF) in a polynomial?
2. Can you explain how to factor polynomials with higher powers of \(x\)?
3. How does factoring help in simplifying polynomial expressions?
4. Can this expression be further factored, and if so, how?
5. What are common methods to factor complex polynomials like this one?

**Tip:** Factoring simplifies expressions and helps solve equations more easily by reducing their complexity.

Factor the expression 3x^56 - 15x^58 + 12x^60.

Learn how to factor the polynomial expression 3x^56 - 15x^58 + 12x^60 by identifying the greatest common factor (GCF). This detailed explanation simplifies higher-order polynomials and is suitable for high school students (Grades 10-12).

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