The value of k , so that x4−3x3+5x2−33x+k  is divisible by x2−5x+6  is

Let the given equation is f(x)=x4−3x3+5x2−33x+k= 0 ….. ( 1 ) Eq. ( 1 ) is divisible by x2−5x+6  The factors of given x2−5x+6  are ⇒(x−2)(x−3)=0 ⇒x=2,x=3 Put x=2  ( or ) x=3  in Eq. ( 1 )⇒f(2)=24−3(2)3+5(2)2−33(2)+k=0 ⇒k=54