To factor out the greatest common factor (GCF) from the expression [tex]\(36c^5 + 54c^8\)[/tex], follow these steps:
1. Identify the GCF of the coefficients:
- The coefficients in the expression are 36 and 54. The greatest common factor (GCF) of 36 and 54 is 18.
2. Identify the GCF of the variable terms:
- The variables in the expression are [tex]\(c^5\)[/tex] and [tex]\(c^8\)[/tex]. The GCF of [tex]\(c^5\)[/tex] and [tex]\(c^8\)[/tex] is [tex]\(c^5\)[/tex]. This is because [tex]\(c^5\)[/tex] is the highest power of [tex]\(c\)[/tex] that divides both [tex]\(c^5\)[/tex] and [tex]\(c^8\)[/tex].
3. Combine the GCFs:
- Combining the GCF of the coefficients (18) with the GCF of the variable terms ([tex]\(c^5\)[/tex]), we get the overall GCF of the expression, which is [tex]\(18c^5\)[/tex].
4. Factor out the GCF from the original expression:
- To factor out [tex]\(18c^5\)[/tex] from [tex]\(36c^5 + 54c^8\)[/tex], divide each term by [tex]\(18c^5\)[/tex]:
[tex]\[
36c^5 \div 18c^5 = 2
\][/tex]
[tex]\[
54c^8 \div 18c^5 = 3c^3
\][/tex]
- Therefore, when factorizing the entire expression by [tex]\(18c^5\)[/tex], we are left with:
[tex]\[
36c^5 + 54c^8 = 18c^5(2 + 3c^3)
\][/tex]
Thus, the factored form of the expression [tex]\(36c^5 + 54c^8\)[/tex] is:
[tex]\[
18c^5(2 + 3c^3)
\][/tex]
This confirms the correct answer.
