Question

a volume of a box is x cube minus 7 x square + 12 x the width of the box is 3 minus x find out volume of the box when X is equals to 1 find the maximum value​

Answer 1

Answer:

V(x) = x3 + 2x2 - 11x - 12

 

To factor, you want 3 numbers that multiply to give -12 (the constant term) and add to give 2 (coefficient of the x2 term).  The answer is 4, -3, and 1: (4)(-3)(1) = -12, 4 + (-3) + 1 = 2.  So the volume polynomial factors to:

 

V(x) = (x+4)(x-3)(x+1)

 

Now the volume of a rectangular box is:

 

V = Length*Width*Height = (x+4)(x-3)(x+1)

 

So let's pick height = (x+1) = 4.5  (you could pick any one of the three factors).

 

x+1 = 4.5

x = 3.5

 

Length = (x+4) = 3.5+4 = 7.5

Width = (x-3) = 3.5 - 3 = 0.5

 

The box's dimensions are 7.5 m by 0.5 m by 4.5 m

Step-by-step explanation:

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