Question

a polynomial and classify polynomials. column, not both:
a. for the following polynomial.
$3x^2y^6 - x^3y^5 - 7 + 4x^5y^3$
identify:
the coefficients:
the degree:
the constant term:
name of the polynomial:
b. give an example of a trinomial that has a
degree of 6, has at least 3 different variables,
and has no constant term:

Explanation:

Step1: Identify coefficients

Coefficients are the numerical factors of each term: $3, -1, 4$

Step2: Calculate term degrees

For $3x^3y^2$: $3+2=5$; for $-x^4y^2$: $4+2=6$; for $4x^2y^3$: $2+3=5$. The highest degree is 6.

Step3: Locate constant term

The constant term is the term without variables: $-7$

Step4: Classify polynomial

It has 4 terms, so it is a quadrinomial (or polynomial with 4 terms).

Step5: Create valid trinomial

Need 3 terms, degree 6, ≥3 variables, no constant term. Example: $2a^3b^2c + 5x^6y - 3z^4w^2$

Answer:

a.

• The coefficients: $3, -1, 4$
• The degree: $6$
• The constant term: $-7$
• Name of the Polynomial: Quadrinomial (4-term polynomial)

b.
$2a^3b^2c + 5x^6y - 3z^4w^2$ (or any equivalent valid trinomial meeting the criteria)