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The value of [tex]b[/tex] in the cubic polynomial is -4.
After a quick analysis, we find that given cubic function is equivalent to the following equivalence:
[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = (x-1)^{2}\cdot (x-2)[/tex]
[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = (x^{2}-2\cdot x + 1)\cdot (x-2)[/tex]
[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-2\cdot x^{2}+x-2\cdot x^{2}+4\cdot x-2[/tex]
[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-4\cdot x^{2}+5\cdot x -2[/tex]
After a quick observation, we conclude that the value of [tex]b[/tex] in the cubic polynomial is -4. [tex]\blacksquare[/tex]
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