SOLUTION: The polynomial x^3 + 5x^2 - ­57x -­189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in. If the width of the box is 15 in., what are the other

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial x^3 + 5x^2 - ­57x -­189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in. If the width of the box is 15 in., what are the other       Log On


   

Question 1036216: The polynomial x^3 + 5x^2 - ­57x -­189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in. If the width of the box is 15 in., what are the other two dimensions? ( Hint: The height is greater than the depth.)

A.
height: 19 in.
depth: 5 in
B.
height: 21 in.
depth: 5 in.
C.
height: 19 in.
depth: 7 in.

D.
height: 21 in.
depth: 7 in.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use polynomial division to divide x%5E3+%2B+5x%5E2+-+57x+-+189 over x%2B5 to find that

%28x%5E3+%2B+5x%5E2+-+57x+-+189%29%2F%28x%2B3%29=x%5E2%2B2x-63

Now factor x%5E2%2B2x-63 to get %28x%2B9%29%28x-7%29

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So all this means x%5E3+%2B+5x%5E2+-+57x+-+189 factors to %28x%2B3%29%28x%2B9%29%28x-7%29

where

width = x+3
height = x+9
depth = x-7

The height is greater than the depth (given in instructions) so because x+9 is larger than x-7, this tells us which expressions go where.

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We're given "the width is (x+3) in....the width of the box is 15 in" which means

x+3 = 15
x+3-3 = 15-3
x = 12

Now we finally know the value of x. We can use this to find the other dimensions.

width = x+3 = 12+3 = 15
height = x+9 = 12+9 = 21
depth = x-7 = 12-7 = 5

The three dimensions of this shipping box are
width = 15 inches
height = 21 inches
depth = 5 inches

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Final Answer:


B.
height: 21 in.
depth: 5 in.