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Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
The temperature of soup after 25 minutes is
<em><u>Solution:</u></em>
The temperature of chicken soup is 192.7°F
As it cools, the temperature of the soup decreases 2.3°F per minute
Let the initial temperature be
Let "t" be the time for rate of decrease
Set up an equation
Temperature = Initial temperature - decrease in temperature
Decrease in temperature = rate of decrease x time
Therefore,
<em><u>To find the temperature of soup after 25 minutes, substitute t = 25</u></em>
Thus the temperature of soup after 25 minutes is