The length of a rectangle is represented by the polynomial 2x^3 -5x^2 +8 and the width is represented
by the polynomial x + 3. Complete the following statements about the polynomial that represents the
area of the rectangle
The polynomial has:
The constant term of the polynomial
The polynomial has a degree of
The leading coefficient of the polynomial is
The constant term of the polynomial representing the area of the rectangle can be found by multiplying the constant terms of the polynomials representing the length and width. In this case, the constant term of the length polynomial is 8 and the constant term of the width polynomial is 3. Therefore, the constant term of the polynomial representing the area is 8 * 3 = 24.
The degree of the polynomial representing the area of the rectangle is found by adding the degrees of the polynomials representing the length and width and then subtracting 1. In this case, the degree of the length polynomial is 3 and the degree of the width polynomial is 1. Therefore, the degree of the polynomial representing the area is 3 + 1 - 1 = 3.
The leading coefficient of the polynomial representing the area of the rectangle is found by multiplying the leading coefficients of the polynomials representing the length and width. In this case, the leading coefficient of the length polynomial is 2 and the leading coefficient of the width polynomial is 1. Therefore, the leading coefficient of the polynomial representing the area is 2 * 1 = 2.