Questions: Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial. x^3 y^2-2 x^3 y^5+5 y-3 The coefficient of the first term is 1. The degree of the first term is 5. The coefficient of the second term is -2. The degree of the second term is 8. The coefficient of the third term is 5. The degree of the third term is 1. The coefficient of the fourth term is -3. The degree of the fourth term is.

Solution Steps

The polynomial is: \[ x^{3} y^{2} - 2 x^{3} y^{5} + 5 y - 3 \]

• First term: \(x^{3} y^{2}\)

  • Coefficient: \(1\)
  • Degree: \(3 + 2 = 5\)

• Second term: \(-2 x^{3} y^{5}\)

  • Coefficient: \(-2\)
  • Degree: \(3 + 5 = 8\)

• Third term: \(5 y\)

  • Coefficient: \(5\)
  • Degree: \(1\)

• Fourth term: \(-3\)

  • Coefficient: \(-3\)
  • Degree: \(0\) (since it is a constant term)

The degree of the polynomial is the highest degree among its terms. From the degrees calculated above:

• The highest degree is \(8\) (from the second term).

Thus, the degree of the polynomial is \(8\).

The leading term is the term with the highest degree, which is \(-2 x^{3} y^{5}\).
The leading coefficient is the coefficient of the leading term, which is \(-2\).

Final Answer