# How do you find the zeros of the function f(x)=(x^3+x^2−6x)/(x−1)?

How do you find the zeros of the function $f\left(x\right)=\frac{{x}^{3}+{x}^{2}-6x}{x-1}$?
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ivice7u
the zeros are the values of x that make f(x)=0
$\text{The denominator of}\phantom{\rule{1ex}{0ex}}f\left(x\right)\ne 0$
as this would make f(x) undefined
equate the numerator to zero and solve
$⇒{x}^{3}+{x}^{2}-6x=0\to \phantom{\rule{1ex}{0ex}}\text{factor out x}$
$⇒x\left({x}^{2}+x-6\right)=0$
$⇒x\left(x+3\right)\left(x-2\right)=0$
$⇒x=0,x=-3,x=2←\phantom{\rule{1ex}{0ex}}\text{are the zeros}$