What no. should be subtracted from x^3+4x2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3? Options:
A) 38
B) 42
C) 46
D) 49
E) 62

Rationale: according to remainder theorem when dfracf ( x ) x + adfracf ( x ) x + a , then the remainder is f ( − a ) f ( − a ) . in this case , as x + 3 x + 3 divides x 3 + 4 x 2 − 7 x + 12 – kx 3 + 4 x 2 − 7 x + 12 – k perfectly ( kk being the number to be subtracted ) , the remainder is 0 when the value of xx is substituted by - 3 . i . e . , ( − 3 ) 3 + 4 ( − 3 ) 2 − 7 ( − 3 ) + 12 − k = 0 ( − 3 ) 3 + 4 ( − 3 ) 2 − 7 ( − 3 ) + 12 − k = 0 or − 27 + 36 + 21 + 12 = k − 27 + 36 + 21 + 12 = k or k = k = 42 b
Answer: B