Question

Find the zeroes of the polynomials.
$x^3-2x^3-x+2$

Answer 1

Let $p\left(x\right)=x^3-2x^3-x+2$
The coefficient of the leading term is $1$ and the constant term is $2.$
Also the factors of $2$ are $1$ and $2.$
So the possible integral zeroes of $p\left(x\right)$ are $\pm 1$ and $\pm 2.$
$p\left(1\right)=(1{)}^3-2(1{)}^3-\left(1\right)+2$
$=1-2-1+2=0$
$\Rightarrow 1$ is a zero of $p\left(x\right).$
Also
$p(-1)=(-1{)}^3-2(-1{)}^3-(-1)+2$
$=-1-2+1+2=0$
$\Rightarrow -1$ is a zero of $p\left(x\right).$
$p\left(2\right)=(2{)}^3-2(2{)}^2-\left(2\right)+2$
$=8-8-2+2=0$
$\Rightarrow 2$ is a zero of $p\left(x\right).$
$\therefore -1,1$ and $2$ are zeroes of $p\left(x\right).$