Algebraic Expressions, I need help!

Question

the volume of box is represented by: V= X³ + 3x² -34x -120. The width is (x - 4) inches. Find an algebraic expression for the other 2 dimensions. The height is greater than the length.

Answer 1

You probably mean that the width is x + 4, since x - 4 is not a factor (x = 4 is not a root).

 

4³ + 3·4² - 34·4 - 120 = -144 ≠ 0.

 

So let's assume you meant x+4.

 

To jet them, just divide V by the given dimension x + 4, then factor the resulting quadratic.

 

V = x³ + 3x² - 34x - 120

 

= x³ + 4x² - x² - 4x - 30x - 120

 

= x²(x + 4) - x(x + 4) - 30(x + 4)

 

= (x² - x - 30)(x + 4)

 

= (x + 5)(x - 6)(x + 4)

 

We want H > L.

 

So the dimensions are

 

W = x + 4

 

L = x - 6

 

H = x + 5