Question

find the degree of the given polynomial and determine whether the polynomial is a monomial, binomial, trinomial, or none of these.

$5xz - 8xz^2 + 6x^3z^3$

the degree of the polynomial is \\(square\\).

is $5xz - 8xz^2 + 6x^3z^3$ a monomial, binomial, trinomial, or none of these?

\\(\circ\\) monomial
\\(\circ\\) binomial
\\(\circ\\) trinomial
\\(\circ\\) none of these

Explanation:

Step1: Find the degree of each term

• For the term \(5xz\): The exponents of \(x\) is \(1\) and \(z\) is \(1\), so the degree is \(1 + 1=2\).
• For the term \(-8xz^{2}\): The exponent of \(x\) is \(1\) and \(z\) is \(2\), so the degree is \(1+2 = 3\).
• For the term \(6x^{3}z^{3}\): The exponent of \(x\) is \(3\) and \(z\) is \(3\), so the degree is \(3 + 3=6\).

Step2: Determine the degree of the polynomial

The degree of a polynomial is the highest degree of its terms. So the degree of \(5xz-8xz^{2}+6x^{3}z^{3}\) is \(6\).

Step3: Classify the polynomial by the number of terms

• A monomial has \(1\) term, a binomial has \(2\) terms, and a trinomial has \(3\) terms. The polynomial \(5xz - 8xz^{2}+6x^{3}z^{3}\) has \(3\) terms, so it is a trinomial.

Answer:

The degree of the polynomial is \(6\), and it is a trinomial.