In each of the following, use factor theorem to find whether polynomial $g(x)$ is a factor of polynomial $f(x)$ or, not.$f(x) = x^3 - 6x^2 + 11x - 6; g(x) = x - 3$
Given:
$f(x) = x^3 - 6x^2 + 11x - 6; g(x) = x - 3$
To do:
We have to find whether polynomial $g(x)$ is a factor of polynomial $f(x)$ or, not.
Solution:
We know that, if $g(x)$ is a factor of $f(x)$, then the remainder will be zero.
$f(x) = x^3 - 6x^2 + 11x - 6; g(x) = x - 3$
So, the remainder will be $f(3)$.
$f(3) = (3)^3-6(3)^2 +11(3)-6$
$= 27 - 6(9) +33-6$
$=60-60$
$=0$
Therefore, $g(x)$ is a factor of polynomial $f(x)$.
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