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Factor out the GCF: [tex]\(36c^5 + 54c^8\)[/tex]

A. [tex]\(18c^5(2 + 3c^3)\)[/tex]
B. [tex]\(18c^3(2c^2 + 3c^5)\)[/tex]
C. [tex]\(3c(12c^4 + 18c^7)\)[/tex]
D. [tex]\(18c^2(2c^3 + 3c^4)\)[/tex]

Sagot :

GinnyAnsweridn
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.
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