Question

6a. Suppose you need to find a box that you can fit your cube-shaped gift into. You know that you will need to find a box that is 4 inches longer than the cube’s length, 3 inches wider than the cube’s width, and 7 inches taller than the cube’s height. Create a polynomial that represents the gift box’s volume in terms of the cube’s length/width/height, in factored and standard form

Answer 1

( l + 4) * ( w + 3 ) * ( h + 7)

let l represent the length, w represent the width, and h represent the height of your cub-shaped gift.

Though, if your gift is in the shape of a cube, that would mean all the sides are the same length.

( 2 + 4 ) * ( 2 + 3 ) * ( 2 + 7 )

6 * 5 * 9 = 270

(I haven't done geometry in awhile though, so this may be incorrect unless it actually makes sense.)

Answer 2

V = (x+ 4)(x + 3)(x + 7); V = x³ + 14x² + 61x + 84

Explanation:

Let x = the side of the cube

Then the dimensions of the gift box are

l = x + 4

w = x + 3

h = x+ 7

V = lwh

V = (x+ 4)(x + 3)(x + 7) Multiply the first two terms

V = (x² + 7x + 12)(x+ 7) Remove parentheses

V = x³ + 14x² + 61x + 84