Question

If $(y-1)$ is a factor of $9y^2+my$, then find the value of $m$

Answer 1

Let $g\left(y\right){=}^{-1}$

$\therefore g\left(y\right)=0$ (xero of polynomial)

or, $y^{-1}=0\Rightarrow y=1$

Now, $f\left(y\right)=9y^2+my$

or, $f\left(1\right)=9(1{)}^2+m(1)=9+m$

$\because g\left(y\right)$ is a factor of $f\left(y\right)$

$\therefore f\left(1\right)=0\Rightarrow 9+m=0\Rightarrow m=-9$