Question
Wed September 12, 2012 By:

I wasn't able to get the solution? I have underlined from where on-wards I didn't got the solution. Why was (x^2 + x - 12) was multiplied with (x - 7) ? Hope you help me ASAP.

Expert Reply
Wed September 12, 2012

s(x) = (x2 + x -12) x quotient

So, s(x) = (x2 + x - 12)(x - 7) or (x - 7) (x2 + x - 12)

OR, s(x) =x (x2 + x - 12) - 7(x2 + x - 12)

OR, s(x) =x3+ x2 – 12x - 7x2  - 7x + 84

OR, s(x) = x3 + x2 - 7x2 - 12x - 7x + 84

OR, s(x) = x3 - 6x2 - 19x + 84                                      … (1)

 

Already s(x) has been found as

s(x) = x3 - 6x2 - (15 + a)x + (80 - b)                             … (2)

 

From (1) and (2);

x3 - 6x2 - (15 + a)x + (80 - b) = x3 - 6x2 - 19x + 84  

 

Equating the coefficients of x and constant term in both sides;

- (15 + a) = - 19 and 80 - b = 84        

OR, -15 - a = - 19 and 80 - b = 84

OR, - a = - 19 + 15 = -4 and - b = 84 - 80 = 4

OR, a = 4 and b = -4

Therefore, if in p(x) we subtracted 4x - 4 then it is exactly divisible by

x2 + x -12.

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