on dividing x3-3 X2 +x+2 by a polynomial g(x) the quotient and remainder were x-2 and -2x+4 respectively find g(x)
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let f(x)=x^3-3 x^2+x+2
q(x)=x-2
r(x)=-2 x+4
g(x)=?
we know that,
f(x)=g(x)*q(x)+r(x)
g(x)=[f(x)-r(x)]/q(x)
= (x^3-3 x^2+x+2+2 x-4)/x-2
=(x^3-3 x^2+3 x-2)/x-2
=x^2-x+1
The value of g(x) is x^2-x+1
q(x)=x-2
r(x)=-2 x+4
g(x)=?
we know that,
f(x)=g(x)*q(x)+r(x)
g(x)=[f(x)-r(x)]/q(x)
= (x^3-3 x^2+x+2+2 x-4)/x-2
=(x^3-3 x^2+3 x-2)/x-2
=x^2-x+1
The value of g(x) is x^2-x+1
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