Question

1. write the polynomial in standard form, identify the degree and leading coefficient of the polynomial, then classify the polynomial by the number of terms. 8d - 2 - 4d³

Explanation:

Step1: Write in Standard Form

Standard form of a polynomial arranges terms in descending order of exponents. For \(8d - 2 - 4d^{3}\), reorder terms: \(-4d^{3}+8d - 2\).

Step2: Identify the Degree

The degree is the highest exponent of the variable. Here, the highest exponent is \(3\) (from \(-4d^{3}\)), so degree is \(3\).

Step3: Identify Leading Coefficient

Leading coefficient is the coefficient of the term with the highest degree. The term with highest degree is \(-4d^{3}\), so leading coefficient is \(-4\).

Step4: Classify by Number of Terms

Count the terms: \(-4d^{3}\), \(8d\), \(-2\) – three terms. A polynomial with three terms is a trinomial.

Answer:

• Standard form: \(\boldsymbol{-4d^{3}+8d - 2}\)
• Degree: \(\boldsymbol{3}\)
• Leading coefficient: \(\boldsymbol{-4}\)
• Classification: \(\boldsymbol{\text{Trinomial}}\)