Question

Delilah needs to design boxes with a volume of 21x^{2} +14x-35. The dimensions of the product within the boxes restrict the length of the boxes to 7 and the height of the boxes to x-1. What will be the width of the boxes?

a) 3x^{2}+2x-5
b) 2x+35
c) 2x-35
d) 3x-5
e) 3x+5

Answer 1

(e) 3x +5

Explanation:

You want the width of a box if its volume is 21x² +14x -35, its length is 7, and its height is x-1.

Factors

The volume can be factored as ...

21x² +14x -35 = 7(3x² +2x -5) = 7(3x +5)(3x -3)/3 = 7(x -1)(3x +5)

The volume is the product of length, width, and height. If length and height are 7 and (x-1), then width is the remaining factor: 3x +5.

The width of the boxes is 3x +5.

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