Answer :

Sure! Let's factor the expression [tex]\(60x^3 + 50x^5\)[/tex] completely, step by step.

1. Identify the Greatest Common Factor (GCF):
First, we need to find the greatest common factor of the terms.

- The coefficients of the terms are 60 and 50. The GCF of 60 and 50 is 10.
- The variable part has [tex]\(x^3\)[/tex] and [tex]\(x^5\)[/tex]. The smallest power of [tex]\(x\)[/tex] in both terms is [tex]\(x^3\)[/tex].

Therefore, the GCF of the entire expression is [tex]\(10x^3\)[/tex].

2. Factor out the GCF:
We factor out [tex]\(10x^3\)[/tex] from each term:

[tex]\[
60x^3 + 50x^5 = 10x^3(6) + 10x^3(5x^2)
\][/tex]

3. Rewrite and combine the expression:
After factoring out [tex]\(10x^3\)[/tex], the expression becomes:

[tex]\[
10x^3(6 + 5x^2)
\][/tex]

4. Check the inner expression:
The expression inside the parentheses, [tex]\(6 + 5x^2\)[/tex], cannot be factored further because 6 and 5x^2 share no common factors and does not fit any special factoring patterns like difference of squares.

So, the completely factored form of the expression [tex]\(60x^3 + 50x^5\)[/tex] is:

[tex]\[
10x^3(5x^2 + 6)
\][/tex]

And that's the final answer.

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