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Find the greatest common factor among the terms in the following polynomial expression. The coefficient of the GCF must be positive.

[tex]\[ 16xy^3 + 28xy^2 + 36x^4y^4 \][/tex]

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GinnyAnsweridn
To find the greatest common factor (GCF) of the terms in the polynomial expression [tex]\(16xy^3 + 28xy^2 + 36x^4y^4\)[/tex], we'll proceed step by step.

1. Identify the GCF of the coefficients:
- The coefficients of the terms are 16, 28, and 36.
- The GCF of these coefficients is 4.

2. Identify the variables and their powers:
- Each term contains the variable [tex]\(x\)[/tex].
- The powers of [tex]\(x\)[/tex] in these terms are 1, 1, and 4, respectively.
- The smallest power of [tex]\(x\)[/tex] is 1.
- Each term contains the variable [tex]\(y\)[/tex].
- The powers of [tex]\(y\)[/tex] in these terms are 3, 2, and 4, respectively.
- The smallest power of [tex]\(y\)[/tex] is 2.

3. Combine the GCF of the coefficients with the variables raised to their respective smallest powers:
- For [tex]\(x\)[/tex], the smallest power is 1, so [tex]\(x^1\)[/tex].
- For [tex]\(y\)[/tex], the smallest power is 2, so [tex]\(y^2\)[/tex].

4. Write down the GCF:
- The greatest common factor of the polynomial expression [tex]\(16xy^3 + 28xy^2 + 36x^4y^4\)[/tex] is [tex]\(4x^1y^2\)[/tex].

Therefore, the GCF of the polynomial expression [tex]\(16xy^3 + 28xy^2 + 36x^4y^4\)[/tex] is [tex]\(4x^1y^2\)[/tex].
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