Final answer:
The cost of each box is found by dividing the total amount polynomial (3x^2 + x - 10) by the number of boxes polynomial (x + 2), resulting in a simplified polynomial that represents the cost per box.
Step-by-step explanation:
To find the cost of each box given the total amount for the shipment, represented by the polynomial expression (3x^2 + x - 10), and the number of boxes is (x + 2), we need to divide the total amount by the number of boxes. This is essentially performing polynomial division.
Divide (3x^2 + x - 10) by (x + 2). Although the question did not provide the complete division algorithm, it is clear that the division process would yield a simplified polynomial that would represent the cost per box.
The actual division process would be carried out by finding how many times the divisor (x + 2) goes into the dividend (3x^2 + x - 10), subtracting this from the dividend, and continuing this process with the resulting polynomial until the remainder is less than the degree of the divisor. The quotient obtained will be the cost per box.