   SEARCH HOME Math Central Quandaries & Queries  Question from Angela, a student: The volume of a box that is two inches high can be represented by V=2X^2-20x+32. Find a way to represent the length and width of the box. (Hint: you will need to use factoring). Hi Angela. I'll show you how this is done with a similar problem.

1. I have a 4 cm deep box whose volume can be represented as v = 4a2 - 32a + 60.
Find a way to represent the length and width of the box. (Hint: you will need to use factoring).
1. I will use the hint and try to factor this quadratic. The first step is to look for easy simple factors that go into everything. 4 does.

v = 4(a2 - 8a + 15)

Now I try to factor further what is in the parentheses: a2 - 8a + 15. Since the factor in front of a2 is (implied to be) 1, I simply look for two numbers that multiply together to make +15 and add together to make -8. That's easy: -3 and -5. So I write:

v = 4 (a - 3) (a - 5)

The volume of a box is length x width x depth, so I should see three factors and I do. I was told that the depth of the box is 4 cm, so the other two must be the length and width (it doesn't matter which is which).

So (a - 3) and (a - 5) are the representations for the width and length of the box.

You can solve your question the same way Angela.

Cheers,
Stephen La Rocque     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.