Please solve q56 ?

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Answer 1 · 2018-06-15T08:53:34

The answer is #option (2)#

Apply the remainder theorem

If #(x-a)# is a factor of #f(x)#, then

#f(a)=0#

Otherwise,

#f(a)= "remainder"#

#f(x)=(x^4-x^3+2x-3)g(x)#

If #(x-3)# is a factor of #g(x)+3#

Then,

#g(3)+3=0#

#=>#, #g(3)=-3#

Therefore,

#f(3)=(3^4-3^3+6-3)g(3)#

#f(3)=(81-27+6-3)*-3=57*-3=-171#

The answer is #option (2)#