a rectangular 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 binomial ... V = (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