Determine the degree of each polynomial.
$-3x^2-5x^2{y}^2+y^3$

• A. $5$
• B. $3$
• C. $4$
• D. $9$

Answer: (C)

Verified step by step guidance

1. Identify each term in the polynomial: \(-3x^{2}\), \(-5x^{2}y^{2}\), and \(y^{3}\).
2. For each term, find the degree by adding the exponents of all variables in that term. For example, in \(-3x^{2}\), the degree is \(2\) because the exponent of \(x\) is \(2\).
3. Calculate the degree of the second term \(-5x^{2}y^{2}\) by adding the exponents: \(2\) (from \(x^{2}\)) plus \(2\) (from \(y^{2}\)), which gives a total degree of \(4\).
4. Calculate the degree of the third term \(y^{3}\), which is simply \(3\) since the exponent of \(y\) is \(3\).
5. Determine the degree of the entire polynomial by selecting the highest degree found among all terms, which is the maximum of \(2\), \(4\), and \(3\).