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So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>
- -10 | 1 + 2 - 82 - 28
- ---------------------------
Now firstly, drop the 1:
- -10 | 1 + 2 - 82 - 28
- ↓
- -------------------------
- 1
Next, you are going to multiply -10 and 1, and then combine the product with 2.
- -10 | 1 + 2 - 82 - 28
- ↓ - 10
- -------------------------
- 1 - 8
Next, multiply -10 and -8, then combine the product with -82:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80
- -------------------------
- 1 - 8 - 2
Next, multiply -10 and -2, then combine the product with -28:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80 + 20
- -------------------------
- 1 - 8 - 2 - 8
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
<u>Putting it together, the quotient is </u>
Answer:
(a)
$850.
(b)
$4250.
(c)
$4267.
Step-by-step explanation:
It is given that the value of a new car decreases by about 15% in the first year.
(a)
Now we are asked to find the cost of a car after one year; if we are given the initial value of car=$1000.
As the rate decreases by 15%.
that means we have to pay (100-15)% of the initial amount.
i.e. we have to pay 85% of the initial amount.
Hence the amount one has to pay= 85% of 1000.
which is equal to =85%×1000
⇒ =
Hence, the amount of car after one year when initaial amount is $1000 is:
$850.
(b)
if initial amount=$ 5000
then amount one has to pay after one year:
Hence, the amount of car after one year when initaial amount is $5000 is:
$4250.
(c)
if initial amount=$ 5020
then amount one has to pay after one year:
Hence, the amount of car after one year when initaial amount is $5020 is:
$4267.