Question

answer the questions about the following polynomial.
$-dfrac{1}{9} + 5x^2$

answer attempt 1 out of 2

the expression represents a polynomial with \\(\square\\) terms. the constant term is \\(\square\\), the leading term is \\(\square\\), and the leading coefficient is \\(\square\\).

Explanation:

Step1: Count total polynomial terms

The polynomial $-\frac{1}{9} + 5x^2$ has two distinct terms: $-\frac{1}{9}$ and $5x^2$.

Step2: Identify the constant term

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

Step3: Identify the leading term

Rewrite the polynomial in standard form (descending degree): $5x^2 - \frac{1}{9}$. The first term is the leading term: $5x^2$.

Step4: Identify the leading coefficient

The leading coefficient is the coefficient of the leading term: $5$.

Step5: Classify polynomial by degree

The highest power of $x$ is 2, so it is a quadratic polynomial.

Answer:

The expression represents a quadratic polynomial with $\boldsymbol{2}$ terms. The constant term is $\boldsymbol{-\frac{1}{9}}$, the leading term is $\boldsymbol{5x^2}$, and the leading coefficient is $\boldsymbol{5}$.