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 constant term of the polynomial is
8
11
24
The constant term of the polynomial that represents the area of the rectangle is 24.
Explanation: To find the area of a rectangle, we multiply the length by the width. The polynomial representing the area would be the product of the two given polynomials (2x^3-5x^2+8) and (x+3), which is:
(2x^3-5x^2+8)(x+3)
Expanding this expression gives us:
2x^4 + 6x^3 - 5x^3 - 15x^2 + 8x + 24
Simplifying further gives us:
2x^4 + x^3 - 15x^2 + 8x + 24
The constant term in this polynomial is 24.