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question:find coeff of x^3 in (x-4)*(x-1)*(x+2)*(x+8)*(x+6).sir i want to know shortcut method at earliest

question:find coeff of x^3 in
(x-4)*(x-1)*(x+2)*(x+8)*(x+6).sir i want to know shortcut method at earliest

Grade:11

1 Answers

Pratham Ashish
17 Points
11 years ago

hi,

see the coefficient of x^3 wii be the

   sum of all the terms of form  x * x * X * a * b

we have only to select  a & b  , for this we have to select two  terms from (x-4)*(x-1)*(x+2)*(x+8)*(x+6).

 these can be

   ( -4 *-1 )   or (-4 *2 ) or ( 2 * 8 ).................

adding all such terms

  gives ,    4  -8  -32  -24 -2 -8 -6 +16 +12 +48

      = 0

so the coeff. of x^3 is 0

 

 

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