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$g(x)=x^4+0.5x^3-11.5x^2-2x+30$

is $x-4$ a factor of $g(x)$ ?

I can't figure out how to factor this out to see if $x-4$ is a factor

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  • $\begingroup$ If you plug in x=4 and the result is y=0, then x-4 is a factor. Google how to factor polynomials. $\endgroup$ – Jonathan Oct 7 '15 at 17:34
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    $\begingroup$ You could also use synthetic division. If the remainder is 0, it is a factor. $\endgroup$ – user277943 Oct 7 '15 at 17:38
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$(X-4)$ is a factor of $g$ if and only if $g(4)=0$; here we have $g(4)=126\neq 0$, so $(X-4)$ is not a factor of $g$.

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$x-4$ is a factor of $g(x)$ if and only if $g(4)=0$, in other words 4 is a root of $g$. Since $$g(4) = 4^4 + 0.5\cdot 4^3 - 11.5\cdot 4^2 - 2\cdot 4 + 30 = 126$$

$x-4$ is not a factor of $g(x)$.

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