Question

1. word bank: linear - quadratic - cubic - quartic - quintic

answer the questions about the following polynomial.
$8x^{4}-x+6x^{2}+\frac{1}{9}$
the expression represents a $\boldsymbol{\square}$ polynomial with $\boldsymbol{\square}$ terms. the constant term is $\boldsymbol{\square}$, the leading term is $\boldsymbol{\square}$, and the leading coefficient is $\boldsymbol{\square}$.

Explanation:

Step1: Classify polynomial by degree

First, rewrite the polynomial in standard form (descending powers of $x$): $8x^4 + 6x^2 - x + \frac{1}{9}$. The highest power of $x$ is 4, so it is a quartic polynomial.

Step2: Count the number of terms

Each separated term by $+$ or $-$ is a term: $8x^4$, $6x^2$, $-x$, $\frac{1}{9}$. That is 4 terms.

Step3: Identify the constant term

The constant term is the term without $x$, which is $\frac{1}{9}$.

Step4: Identify the leading term

The leading term is the term with the highest power of $x$, which is $8x^4$.

Step5: Identify the leading coefficient

The leading coefficient is the coefficient of the leading term, which is 8.

Answer:

The expression represents a $\boldsymbol{quartic}$ polynomial with $\boldsymbol{4}$ terms. The constant term is $\boldsymbol{\frac{1}{9}}$, the leading term is $\boldsymbol{8x^4}$, and the leading coefficient is $\boldsymbol{8}$.