High School

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Factor the expression completely:

[tex]\[ 5 - 45x^5 \][/tex]

Answer :

We start with the expression

[tex]$$
5 - 45x^5.
$$[/tex]

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

Notice that both terms share a common factor of [tex]$5$[/tex]. Factoring [tex]$5$[/tex] out gives

[tex]$$
5 - 45x^5 = 5(1 - 9x^5).
$$[/tex]

Step 2. Rewriting the Expression:

The expression inside the parentheses, [tex]$1 - 9x^5$[/tex], can be rewritten by factoring out a negative sign. That is,

[tex]$$
1 - 9x^5 = -(9x^5 - 1).
$$[/tex]

Substitute this back into the factored expression:

[tex]$$
5(1 - 9x^5) = 5\bigl[-(9x^5 - 1)\bigr] = -5(9x^5 - 1).
$$[/tex]

Thus, the completely factored form of the given expression is

[tex]$$
-5(9x^5 - 1).
$$[/tex]>

This is the final answer.

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