Answer :

We start with the expression
[tex]$$
-45 - 50x^4.
$$[/tex]

Step 1. Identify the Greatest Common Factor (GCF):

The coefficients are 45 and 50, and their greatest common factor is 5. Since both terms are negative and we wish to have a positive expression inside the parentheses, we factor out [tex]$-5$[/tex].

Step 2. Factor Out [tex]$-5$[/tex]:

Dividing each term by [tex]$-5$[/tex]:
- For the first term:
[tex]$$
\frac{-45}{-5} = 9,
$$[/tex]
- For the second term:
[tex]$$
\frac{-50x^4}{-5} = 10x^4.
$$[/tex]

Thus, the expression becomes
[tex]$$
-45 - 50x^4 = -5(9 + 10x^4).
$$[/tex]

Step 3. Write the Final Factored Form:

The completely factored expression is
[tex]$$
-5(9 + 10x^4).
$$[/tex]

This concludes the step-by-step factorization of the given expression.

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