Arectangular box is 24 in. long, 12 in wide, and 18 in high. if each dimension is increased by x in .. write a polynomial function in standard form modeling the volume of the box

V = x³ + 54x² + 936x + 5,184

Step-by-step explanation:

If we add a value of 'x' to each side of the box, the new dimensions can be represented asx + 24x + 12 and x + 18To find the volume of the new box, multiply all of the dimensions togetherV = (x + 24)(x + 12)(x + 18)     Foil the first and second binomialV = (x² + 36x + 288)(x + 18)  Now multiply the two polynomials together...V = x²(x) + 36x(x) + 288x + x²(18) + 36x(18) + 288(18)V = x³ + 36x² + 288x + 18x² + 648x + 5,184which simplifies toV = x³ + 54x² + 936x + 5,184     where x represents the increase in inches