Question

Let g(x) = (3x + 4)(x - 1)(x - 3) be a polynomial function. What is the degree of the polynomial?

A. Degree is 1.
B. Degree is 2.
C. Degree is 3.
D. Degree is 4.
What is the sign of the leading coefficient?
A. Positive
B. Negative
C. Zero
D. Undefined

Answer 1

The degree of the polynomial is 3 and the sign of the leading coefficient is positive.

Step-by-step explanation:

The degree of a polynomial function is determined by the highest power of x in the polynomial. In this case, the polynomial function g(x) = (3x + 4)(x - 1)(x - 3) has three factors, each of which includes x raised to the power of 1. Therefore, the degree of the polynomial is 3. Therefore, the correct answer is C. Degree is 3.

The leading coefficient is the coefficient of the term with the highest power of x. In this case, the term with the highest power of x is 3x^3. Therefore, the leading coefficient is 3, which is positive. Therefore, the correct answer is A. Positive.