f(x) = x^3 - 6x² + 11x – 6, g(x) = x² – 3x+2
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As f(1),f(2) is Zero . Therefore g(x) is the factor of polynomial f(x)
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Answer:
g(x)=x^2-3x+2
=x^2-2x-x+2
=x(x-2) -1(x-2)
=(x-1) (x-2)
So,we get two value of x
that is (x-1) (x-2)
f(x)=x^3-6x^2+11x-6 (x=1)
f(1) =(1)^3-6(1)^2+11(1)-6
=1-6(1)+11-6
=1-6+11-6
=(-5)+11-6
=6-6
f(1) =0
f(x)=x^3-6x^2+11x-6 (x=2)
f(2)=(2)^3-6(2)^2+11(2)-6
=8-6(4)+22-6
=8-24+22-6
=(-16)+22-6
=6-6
f(2)=0
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