Question

give the degree of the polynomial
$-3x^{9}+3 - 15x^{4}uv^{3}+v^{3}x^{2}$

Explanation:

Step1: Recall the degree of a term

The degree of a term with multiple variables is the sum of the exponents of the variables in that term.

Step2: Analyze each term

• For the term \(-3x^{9}\), the degree is \(9\) (only \(x\) with exponent \(9\)).
• For the term \(-3\) (a constant), the degree is \(0\) (since there are no variables).
• For the term \(-15x^{4}uv^{3}\), the exponents of \(x\), \(u\), \(v\) are \(4\), \(1\), \(3\) respectively. So the degree is \(4 + 1+ 3=8\).
• For the term \(v^{3}x^{2}\) (which is \(x^{2}v^{3}\)), the exponents of \(x\) and \(v\) are \(2\) and \(3\) respectively. So the degree is \(2 + 3 = 5\).

Step3: Determine the degree of the polynomial

The degree of a polynomial is the highest degree among all its terms. Comparing the degrees \(9\), \(0\), \(8\), and \(5\), the highest is \(9\).

Answer:

\(9\)