Will give medal. 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.
I got this question wrong on a quiz, I thought it was C, but it was wrong. Does anyone know the correct answer?

Question

Will give medal. 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.
I got this question wrong on a quiz, I thought it was C, but it was wrong. Does anyone know the correct answer?

badhi · Answer

Answer is B.

We should be able to express the volume as following
$$x^3+5x^2-57x-189 = (ax+b)(cx+d)(x+3)$$

after finding values for a,b,c,d and substituting the value for x ( ie, its given that x+3 = 15) , you should get answer as B

triciaal · Answer

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