what is the gcf of x^5y^4+x^3y^2+x^2y^3+y

To find the greatest common factor (GCF) of the expression \(x^5y^4 + x^3y^2 + x^2y^3 + y\), we look for the common factors among all terms.

### Given expression:
\[x^5y^4 + x^3y^2 + x^2y^3 + y\]

1. **First term**: \(x^5y^4\)
2. **Second term**: \(x^3y^2\)
3. **Third term**: \(x^2y^3\)
4. **Fourth term**: \(y\)

Now, we identify the common factors between the terms.

- The common factor for all terms in terms of \(x\):
    - The first term has \(x^5\), second has \(x^3\), third has \(x^2\), and the fourth has no \(x\).
    - Therefore, the GCF for \(x\) is **1**, since the last term has no \(x\).

- The common factor for all terms in terms of \(y\):
    - The first term has \(y^4\), second has \(y^2\), third has \(y^3\), and the fourth has \(y\).
    - The GCF for \(y\) is **\(y\)**, since \(y\) is the smallest power present in all terms.

Thus, the greatest common factor (GCF) of the entire expression is:

\[\boxed{y}\]

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Would you like further details or have any questions? Here are five related questions:

1. How do you factor expressions with multiple variables?
2. What is the difference between GCF and LCM in algebra?
3. Can you always find a GCF when factoring polynomials?
4. How would you simplify the original expression after factoring out the GCF?
5. How do you approach factoring in expressions with negative terms?

**Tip**: When factoring expressions, always look for the smallest power of each variable present across all terms.

what is the gcf of x^5y^4 + x^3y^2 + x^2y^3 + y

Learn how to find the greatest common factor (GCF) of the polynomial expression x^5y^4 + x^3y^2 + x^2y^3 + y. This problem covers factoring techniques for polynomials with multiple variables. Suitable for students in Grades 8-10.

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