Answer:
1.33
Step-by-step explanation:
4/3
The correct factorization is (p + 16)(p + 2).
You can find this by looking for factors of the final number that add up to the middle number. Factors of the final number are listed below:
1 * 32
-1 * -32
2 * 16
-2 * -16
4 * 8
-4 * -8
Now you select the one that adds to 18, which would be the highlighted 2 and 16. Now we use these in parenthesis with a p + in the front of it.
(p + 2)(p + 16)
This will be the correct factored form.
With
we have
so 
has one eigenvalue, 
, with multiplicity 3.
In order for to not be defective, we need the dimension of the eigenspace to match the multiplicity of the repeated eigenvalue 2. But 
has nullspace of dimension 2, since
That is, we can only obtain 2 eigenvectors,
and there is no other. We needed 3 in order to complete the basis of eigenvectors.
The unit rate here is 2 pounds of trash in an hour. If two pounds of trash are picked up in an hour, we can multiply that by 3 and get that there will be 6 pounds picked up in 3 hours.
