If p(x)=x3−5x2+4x−3 and g


If $p(x)=x^{3}-5 x^{2}+4 x-3$ and $g(x)=x-2$, show that $p(x)$ is not a multiple of $g(x)$.


$p(x)=x^{3}-5 x^{2}+4 x-3$


Putting x = 2 in p(x), we get

$p(2)=2^{3}-5 \times 2^{2}+4 \times 2-3=8-20+8-3=-7 \neq 0$

Therefore, by factor theorem, (x − 2) is not a factor of p(x).

Hence, p(x) is not a multiple of g(x).


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