Question

answer the questions about the following polynomial. $-dfrac{1}{9} + 5x^2$ answer attempt 1 out of 3 the expression represents a quadratic polynomial with \\(\square\\) terms. the constant term is \\(\square\\), the leading term is \\(\square\\), and the leading coefficient is \\(\square\\).

Explanation:

Step1: Count the terms

A term is a single number or a variable (or both) multiplied together. In the polynomial $-\frac{1}{9} + 5x^2$, we can identify two terms: $-\frac{1}{9}$ (the constant term) and $5x^2$ (the quadratic term). So the number of terms is 2.

Step2: Identify the constant term

The constant term is the term without a variable. In $-\frac{1}{9} + 5x^2$, the constant term is $-\frac{1}{9}$.

Step3: Identify the leading term

The leading term is the term with the highest degree. For a polynomial in one variable, the degree of a term is the exponent of the variable. Here, the term $5x^2$ has degree 2, and $-\frac{1}{9}$ has degree 0. So the leading term is $5x^2$.

Step4: Identify the leading coefficient

The leading coefficient is the coefficient of the leading term. The leading term is $5x^2$, so its coefficient is 5.

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 $\boldsymbol{5}$.