Answer :

Let's factor the greatest common factor (GCF) out of the polynomial [tex]\(-35x^5 - 25x^3 - 5x^2\)[/tex].

1. Identify the GCF of the coefficients:
- The coefficients of the polynomial are [tex]\(-35\)[/tex], [tex]\(-25\)[/tex], and [tex]\(-5\)[/tex].
- The GCF of 35, 25, and 5 is [tex]\(5\)[/tex].

2. Factor out the GCF from the coefficients:
- Each term of the polynomial includes a coefficient divisible by 5, so we can simplify each term:
- [tex]\(-35x^5\)[/tex] becomes [tex]\(-5 \cdot 7x^5\)[/tex],
- [tex]\(-25x^3\)[/tex] becomes [tex]\(-5 \cdot 5x^3\)[/tex],
- [tex]\(-5x^2\)[/tex] becomes [tex]\(-5 \cdot x^2\)[/tex].

3. Factor out the [tex]\(x^2\)[/tex], the smallest power of [tex]\(x\)[/tex] present in all terms:
- Since each term contains at least [tex]\(x^2\)[/tex], we can factor [tex]\(x^2\)[/tex] out of every term.

4. Combine the factored terms:
- Factoring out [tex]\(-5x^2\)[/tex], the expression becomes:
[tex]\[
-5x^2(7x^3 + 5x + 1)
\][/tex]

Thus, the polynomial [tex]\(-35x^5 - 25x^3 - 5x^2\)[/tex] is factored as [tex]\(-5x^2(7x^3 + 5x + 1)\)[/tex].

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