SOLUTION: 50. A bride-to-be has several girlfriends, but she has decided to have only five bridesmaids, including the maid of honor. The number of different ways n girlfriends can be chosen

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Question 57085This question is from textbook Applied College Algebra
: 50. A bride-to-be has several girlfriends, but she has decided to have only five bridesmaids, including the maid of honor. The number of different ways n girlfriends can be chosen and assigned a position, such as maid of honor, first matron, second matron, and so on, is given by polynomial function
P(n) = n^5 - 10n^4 + 35n^3 - 50n^2 + 24n
a. Use the remainder Theorem to determine the number of ways the bride can select her bridesmaids if she choose from n = 7 girlfriends.
b. Evaluate P(n) for n = 7 by substituting 7 for n. How does this result compare with the result obtained in part a.?This question is from textbook Applied College Algebra

Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!
P(n) = n^5 - 10n^4 + 35n^3 - 50n^2 + 24n
a. Use the remainder Theorem to determine the number of ways the bride can select her bridesmaids if she choose from n = 7 girlfriends.
b. Evaluate P(n) for n = 7 by substituting 7 for n. How does this result compare with the result obtained in part a.?
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a. The Remainder Theorem says the remainder when you divide a polynomial
be n-k is f(k)
You can divide by long division or by synthetic division.
That's a mess when you have to type it so let me just say
you get a quotient of n^4-3n^3+14n^2+48n+360 and a remainder
of 2520
b. Same result
Cheers,
Stan H.