Question

Factor the polynomial.
19 xy Superscript 6 Baseline plus 57 x cubed y Superscript 4
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Part 1
19xy Superscript 6plus57x cubedy Superscript 4equals
  
enter your response here ​(Factor completely.)

Answer 1

To factor the polynomial \( 19xy^6 + 57x^3y^4 \), we can start by identifying the greatest common factor (GCF) of the two terms.

1. **Identify the GCF:**
- The coefficients are 19 and 57. The GCF of 19 and 57 is 19.
- For the variable \( x \), the term \( x \) appears in both, with the lowest power being \( x \).
- For the variable \( y \), the lowest power in the two terms is \( y^4 \).

So, the GCF is \( 19xy^4 \).

2. **Factor out the GCF:**
\[
19xy^6 + 57x^3y^4 = 19xy^4(y^2 + 3x^2)
\]

Thus, the completely factored form is:

\[
19xy^4(y^2 + 3x^2)
\]

So the final answer is:
\[
19xy^4(y^2 + 3x^2)
\]