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? Pick one:  A) 38  B) 42  C) 46  D) 49  E) 62
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+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+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   42
<result>B</result>
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?