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Answer :
Final Answer:
The greatest common factor (GCF) of [tex]\(12x^3\)[/tex] and [tex]\(28x^5\)[/tex] is [tex]\(4x^3\)[/tex].
Explanation:
The greatest common factor (GCF) of two or more terms is the largest factor that divides all of the terms evenly. In this case, we need to find the common factors of both [tex]\(12x^3\)[/tex] and [tex]\(28x^5\)[/tex], and then determine the highest common factor.
The prime factorization of [tex]\(12x^3\)[/tex] is [tex]\(2^2 \cdot 3 \cdot x^3\)[/tex], and the prime factorization of [tex]\(28x^5\) is \(2^2 \cdot 7 \cdot x^5\).[/tex]
The common factors are [tex]\(2^2\)[/tex] and [tex]\(x^3\)[/tex]. To find the GCF, we take the smallest exponent for each common prime factor. Therefore, the GCF is[tex]\(2^2 \cdot x^3 = 4x^3\).[/tex]
Hence, the GCF of [tex]\(12x^3\)[/tex] and [tex]\(28x^5\)[/tex] is [tex]\(4x^3\)[/tex].
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