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Answer:
$12 000 in Portfolio 1 and $13 000 in Portfolio 2
Step-by-step explanation:
The formula for simple interest is
I = Prt
For each portfolio, t = 1 yr
For Portfolio 1, i = 5.25 % = 0.0525
For Portfolio 2, i = 4 % = 0.04
Let x = amount invested in Portfolio 1. Then
25 000 - x = amount invested in Portfolio 2 and
25 000 - x = 25 000 - 12 000 = 13 000
So, $12 000 is invested in Portfolio 1 and $13 000 is invested in Portfolio 2.
Check:
OK.
You can do this by either synthetic division or long division. I choose synthetic because it's easier. Remember, you need the root to do synthetic division, so for the function, the root is at x = -1. Let's set it up:
-1 | 1 0 -3
<u> -1 1</u>
1 -1 -2
These are the coefficients of our depressed polynomial. The polynomial will have 1 less degree in the answer, and it will look like:
As you can see, the remainder by doing that is -2, but in polynomial form you would write it as: 2/x+1. Hopefully, this makes sense to you!
-1 | 1 0 -3
<u> -1 1</u>
1 -1 -2
These are the coefficients of our depressed polynomial. The polynomial will have 1 less degree in the answer, and it will look like:
As you can see, the remainder by doing that is -2, but in polynomial form you would write it as: 2/x+1. Hopefully, this makes sense to you!