Question #cfd96

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Answer 1 · 2017-12-18T03:34:46

As the polynomial has degree #n=3# and #f(3)=0; f(51)=0#

A possible polynomial may be written as #f(x)=(x-3)(x-51)(x+b)#

Again #f(-1)=208#

So #(-1-3)(-1-51)(-1+b)=208#

#=>(-4)(-52)(-1+b)=208#

#=>(-1+b)=208/208=1#
#=>b=2#

So polynomial is

#f(x)=(x-3)(x-51)(x+2)#

#=>f(x)=(x^2-x-6)(x-51)#

#=>f(x)=x^3-x^2-6x-51x^2+51x+306#

#=>f(x)=x^3-52x^2+45x+306#