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Answer :
To factor the expression [tex]\(5 - 45x^5\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
First, we need to find the greatest common factor of the terms in the expression. The terms are [tex]\(5\)[/tex] and [tex]\(-45x^5\)[/tex].
- The GCF of [tex]\(5\)[/tex] and [tex]\(45\)[/tex] is [tex]\(5\)[/tex].
- Both terms do not have [tex]\(x\)[/tex], so there is no [tex]\(x\)[/tex] in the GCF.
Thus, the GCF of the expression is [tex]\(5\)[/tex].
2. Factor Out the GCF:
Next, factor out the GCF from each term in the expression:
[tex]\[
5 - 45x^5 = 5(1) - 5(9x^5)
\][/tex]
This simplifies to:
[tex]\[
5(1 - 9x^5)
\][/tex]
3. Further Factor the Expression:
The expression inside the parentheses, [tex]\(1 - 9x^5\)[/tex], is a difference of terms. However, it cannot be factored further using integers. Therefore, the completely factored form of the original expression is:
[tex]\[
5(1 - 9x^5)
\][/tex]
4. Simplify and Check:
You can check this factorization by distributing the [tex]\(5\)[/tex] back into the expression:
[tex]\[
5 \times 1 - 5 \times 9x^5 = 5 - 45x^5
\][/tex]
This confirms that our factorization is correct.
So, the completely factored expression is:
[tex]\[
-5(9x^5 - 1)
\][/tex]
1. Identify the Greatest Common Factor (GCF):
First, we need to find the greatest common factor of the terms in the expression. The terms are [tex]\(5\)[/tex] and [tex]\(-45x^5\)[/tex].
- The GCF of [tex]\(5\)[/tex] and [tex]\(45\)[/tex] is [tex]\(5\)[/tex].
- Both terms do not have [tex]\(x\)[/tex], so there is no [tex]\(x\)[/tex] in the GCF.
Thus, the GCF of the expression is [tex]\(5\)[/tex].
2. Factor Out the GCF:
Next, factor out the GCF from each term in the expression:
[tex]\[
5 - 45x^5 = 5(1) - 5(9x^5)
\][/tex]
This simplifies to:
[tex]\[
5(1 - 9x^5)
\][/tex]
3. Further Factor the Expression:
The expression inside the parentheses, [tex]\(1 - 9x^5\)[/tex], is a difference of terms. However, it cannot be factored further using integers. Therefore, the completely factored form of the original expression is:
[tex]\[
5(1 - 9x^5)
\][/tex]
4. Simplify and Check:
You can check this factorization by distributing the [tex]\(5\)[/tex] back into the expression:
[tex]\[
5 \times 1 - 5 \times 9x^5 = 5 - 45x^5
\][/tex]
This confirms that our factorization is correct.
So, the completely factored expression is:
[tex]\[
-5(9x^5 - 1)
\][/tex]
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