SOLUTION: Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker (t) hours after starting

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Question 205915This question is from textbook elementary and intermediate algebra
: Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker (t) hours after starting work could be modeled by the formula N(t)=-3t^3+23t^2+8t. Factor the right side of the equation and find N(3). I am completely lost. Please help. This question is from textbook elementary and intermediate algebra

Found 2 solutions by Edwin McCravy, Earlsdon:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker (t) hours after starting work could be modeled by the formula N(t)=-3t^3+23t^2+8t. Factor the right side of the equation and find N(3). I am completely lost. Please help.

N%28t%29=-3t%5E3%2B23t%5E2%2B8t

Factor out out -t:

N%28t%29=-t%283t%5E2-23t-8%29

Factor the expression in parentheses:

N%28t%29=-t%283t%2B1%29%28t-8%29

Now substitute 3 for all t's:

N%283%29=-3%283%2A3%2B1%29%283-8%29
N%283%29=-3%289%2B1%29%28-5%29
N%28t%29=-3%2810%29%28-5%29
N%28t%29=150

Edwin

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
N%28t%29+=+3t%5E3%2B23t%5E2%2B8t
N%28t%29+=+t%283t%5E2%2B23t%2B8%29 ...and that's the best we can do for the factoring part. To find N%283%29, simply substitute t+=+3
N%283%29+=+3%283%283%5E2%29%2B23%283%29%2B8%29
N%283%29+=+3%2827%2B69%2B8%29
N%283%29+=+3%28104%29
highlight%28N%283%29+=+312%29