Michigan State University - Diagnostic Exam

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5.15

  •   The expansion of ( )12 2 2- x - x has 13 terms. Which of the following is the coefficient of the term that does not contain an x?

    a) 212 b) 12 c) -24 d) 126720 e) -101376

Solution:

The general term in the expansion is

( ) ( ) | 12 | ( )r | 12 | | | ( 2)12-r --2 r| | 24-3r |( r |) x x = (- 2) |( r |) x

Notice that 0 r = 8 ⇒ x so that the term we are looking for has coefficient

( ) | 12 | ( ) (- 2)8|| || = 28 12!- = 126720 ( 8 ) 8!4!

Diagnostic:

See 4.16: Binomial Theorem and 5.16: Counting (Permutations and Combinations) .

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July 15, 2008