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Question -

If x3 – 3x2 + 3x – 7= (x + 1) (ax2 + bx + c), then a + b + c =
(a)4                                   
(b)12                             
(c)-10                                 
(d) 3



Answer -

x3 – 3x2 + 3x + 7 = (x + 1) (ax2 +bx + c)
= ax3 + bx2 + cx + ax2 + bx + c
x3 – 3x2 + 3x – 7 = ax3 + (b +a)2 + (c + b)x + c
Comparing the coefficient,
a = 1
b + a = -3 
 b+1=-3  b = -3-1=-4
c + b = 3 
 c-4 = 3  c= 3 + 4 = 7
a + b + c = 1- 4 + 7 = 8- 4 = 4             (a)

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