fagiolinow8xk

2023-02-26

What are the zeros of the polynomial function $f\left(x\right)={x}^{3}–{x}^{2}-12x$?

sarabol2zsr

We have:
$\text{XXX}f\left(x\right)={x}^{3}-{x}^{2}-12x$
Factoring:
$\text{XXX}f\left(x\right)=x\left({x}^{2}-x-12\right)$
$\text{XXXXX}=x\left(x-4\right)\left(x+3\right)$
The instances of $x$ for which a function returns 0 are referred to as its zeroes.
$\text{XXX}f\left(x\right)=x\left(x-4\right)\left(x+3\right)=0$
implies
either
$\text{XXXXX}x=0$
or
$\text{XXXXX}\left(x-4\right)=0\to x=4$
or
$\text{XXXXX}\left(x+3\right)=0\to x=-3$

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