In each of the following, use factor theorem to find whether polynomial $g(x)$ is a factor of polynomial $f(x)$ or, not.$f(x) = x^3 - 6x^2 - 19x + 84, g(x) = x - 7$
Given:
$f(x) = x^3 - 6x^2 - 19x + 84, g(x) = x - 7$
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.
$f(x) = x^3 - 6x^2 - 19x + 84, g(x) = x - 7$
So, the remainder will be $f(7)$.
$f(7) = (7)^3-6(7)^2 -19(7)+84$
$= 343-6(49) -133+84$
$=294-294$
$=0$
Therefore, $g(x)$ is a factor of polynomial $f(x)$.
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