Question

Factor the polynomial.
19 x Superscript 4 Baseline y squared plus 57 x Superscript 5 Baseline y
Question content area bottom
Part 1
19x Superscript 4y squaredplus57x Superscript 5yequals
  
enter your response here ​(Factor completely.)

Answer 1

To factor the polynomial \(19x^4y^2 + 57x^5y\), we 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 \(19\).
- The variable part has \(x^4\) and \(x^5\). The GCF is \(x^4\).
- The variable part has \(y^2\) and \(y\). The GCF is \(y\).

Thus, the greatest common factor (GCF) of the entire expression is \(19x^4y\).

2. **Factor out the GCF:**
Now we will factor out \(19x^4y\) from each term:

- For \(19x^4y^2\):
\[
\frac{19x^4y^2}{19x^4y} = y
\]
- For \(57x^5y\):
\[
\frac{57x^5y}{19x^4y} = 3x
\]
(Note that \(57x^5y = 3 \times 19x^4y\))

Thus, we can rewrite the polynomial as:
\[
19x^4y(y + 3x)
\]

So the fully factored form of the polynomial is:
\[
\boxed{19x^4y(y + 3x)}
\]