Question

Identify the leading coefficient, and classify the polynomial by degree and by number of terms. $$-5 x-4$$

Short answer

The leading coefficient is -5. The polynomial is of degree 1 (linear polynomial), and it's a binomial because it has two terms.

Step-by-step solution

Identify the Terms of the Polynomial

The polynomial mentioned here is \( -5x - 4\). This has two terms which are \( -5x \) and \( -4 \).

Determine the Leading Coefficient

The leading coefficient of a polynomial is the numerical coefficient of the term of highest degree. For this polynomial, the highest degree term is \( -5x \) (degree 1), and its coefficient is \( -5 \). Thus, the leading coefficient is \( -5 \).

Classify the Polynomial by Degree

The degree of a polynomial is the highest power of the variable. Here, the polynomial is first degree since the variable \( x \) is raised to the power of 1 in the term \( -5x \). Thus, this is a first-degree polynomial also known as a linear polynomial.

Classify the Polynomial by Number of terms

The polynomial \( -5x - 4 \) contains two terms. Therefore, it can be classified as a binomial.