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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

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Solution

The given equation is

x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c)

This can be written as

x3-3x2+3x-7=x+1ax2+bx+cx3-3x2+3x-7=ax3+bx2+cx+ax2+bx+cx3-3x2+3x-7=ax3+a+bx2+b+cx+c

Comparing the coefficients on both sides of the equation.

We get,


c = -7 .......(4)

Putting the value of a from (1) in (2)

We get,

So the value of a, b and c is 1, – 4 and -7 respectively.

Therefore,

a + b + c =1 - 4 - 7 = -10

So, the correct choice is (c).


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