18/ (x-1) is a factor of ax +bx+cx+dx*e Show that a+cée bd 0. is diuisible by x2-3x+2.

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( x^{2}-1 ) is a falce of ( cos (x)=a x^{4}+b x^{3} ) ( +c x^{2}+d x+e ) men ( x^{2}-1 ) munt Thus at ( x=1, p(x) ), becmes, ( P(1)=0 ) ( P(1)=a+b+c+d+e=0 quad-0 ) Also ( , quad P(-1)=0 ) ( p(-1)=a-b+c-d+e=0 ) Adding 0 and ( (2, ), we get, ( a+b+c+x+e+a-b+c-d+e=0 ) ( a+c+e+a+c+e=0 ) ( 2(a+c+c)=0 ) ( Rightarrow quad a+c+e=0 ) Subleact (1) and 2 , we get ( a+b+c+d+e-a+b-c+d-e=0 ) ( b+d+b+d=0 ) ( 2(b+d)=0 ) ( b+d=0 ) ( Rightarrow quad a+c+c=b+d=0 )

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