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------------------------------------------------ Factor out the greatest common factor from the expression:

[tex]3x^7 + 12x^5 + 9x^2[/tex]

Sure! Let's go through the process of factoring out the greatest common factor step-by-step:

1. Identify the Terms:
- The expression given is [tex]$3x^7 + 12x^5 + 9x^2$[/tex].

2. Find the Greatest Common Factor (GCF):
- First, look at the coefficients: 3, 12, and 9. The greatest common factor of these numbers is 3.
- Now, look at the variable part. Each term has [tex]$x$[/tex] raised to a power. The smallest exponent is 2 (from [tex]$9x^2$[/tex]), so the greatest common factor for the variable part is [tex]$x^2$[/tex].

3. Factor Out the GCF:
- Since the greatest common factor of the entire expression is [tex]$3x^2$[/tex], we factor this out from each term:
- [tex]$3x^7$[/tex] becomes [tex]$3x^2 \cdot x^5$[/tex],
- [tex]$12x^5$[/tex] becomes [tex]$3x^2 \cdot 4x^3$[/tex],
- [tex]$9x^2$[/tex] becomes [tex]$3x^2 \cdot 3$[/tex].

4. Rewrite the Expression:
- Factoring [tex]$3x^2$[/tex] out of each term, the expression becomes:
[tex]\[
3x^2(x^5 + 4x^3 + 3)
\][/tex]

So, the expression [tex]$3x^7 + 12x^5 + 9x^2$[/tex] factors to [tex]$3x^2(x^5 + 4x^3 + 3)$[/tex].

This step-by-step process shows how to factor out the greatest common factor from the given polynomial.