A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the volume of the delivery box to be 224 cubic inches. If the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be? 3 inches
7 inches
8 inches
4 inches

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Translating the word problem into an algebraic expression;

 ......equation 1

 ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

 .....equation 3.

Substituting the values into equation, we have;

Rearranging the polynomial, we have;

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

We would try with 4;

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

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