Hi Angela. I'll show you how this is done with a similar problem.
- 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).
- 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.
Stephen La Rocque