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Remainder theorem:let p(x)be any polynomial of degree greater than or equal to one and let 'a'be any real number .If p(x)is divided by the linear polynomial (x-a),then the remainder is p(a).

ex:by division algorithm,

p(x)=g(x).q(x)+r(x)

p(x)=(x-a).q(x)+r(x) g(x)=(x-a)

since the degree of(x-a)is 1 and the degree of r(x)is less than the degree of (x-a)

therefore,degree of r(x)=0,implies r(x)is a constant,say K

so,for every real value of x,r(x)=K

therefore,

p(x)=(x-a)q(x)+K

If x=a,then p(a)=(a-a)q(a)+K

=0+K

=K

hence proved.

hope this helps u:))

ex:by division algorithm,

p(x)=g(x).q(x)+r(x)

p(x)=(x-a).q(x)+r(x) g(x)=(x-a)

since the degree of(x-a)is 1 and the degree of r(x)is less than the degree of (x-a)

therefore,degree of r(x)=0,implies r(x)is a constant,say K

so,for every real value of x,r(x)=K

therefore,

p(x)=(x-a)q(x)+K

If x=a,then p(a)=(a-a)q(a)+K

=0+K

=K

hence proved.

hope this helps u:))