Answer :

To factor the expression completely, we start with the given expression:

[tex]\[ -45 - 50x^4 \][/tex]

Here is a step-by-step breakdown of the factoring process:

1. Identify the Greatest Common Factor (GCF):

First, look for the greatest common factor of the coefficients [tex]\(-45\)[/tex] and [tex]\(-50\)[/tex].

- The GCF of 45 and 50 is 5. Since the expression has a negative leading coefficient, we'll factor out [tex]\(-5\)[/tex].

2. Factor Out the GCF:

When we factor out [tex]\(-5\)[/tex] from the expression, we divide each term by [tex]\(-5\)[/tex]:

[tex]\[
\frac{-45}{-5} = 9
\][/tex]

[tex]\[
\frac{-50x^4}{-5} = 10x^4
\][/tex]

Therefore, factoring out the [tex]\(-5\)[/tex] gives:

[tex]\[
-5(9 + 10x^4)
\][/tex]

3. Check for Further Factoring:

The expression inside the parentheses, [tex]\(9 + 10x^4\)[/tex], does not factor any further since there are no common factors, and it is not a recognizable special product like a difference of squares or sum/difference of cubes.

Thus, the completely factored expression is:

[tex]\[
-5(10x^4 + 9)
\][/tex]

This is the final factored form of the expression.

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