Determine the zero's
f(x) = kx^3 - 8x -x +3k + 1 k=3 and has a zero when x = 2
3x^3 - 8x^2 - x + 3(3) + 1
= 3x^3 - 8x^2 - x +10 <<<<< don't know what to do after this step
Hello, Devi09!
$\displaystyle \text{Determine the zeros:}$
. . $\displaystyle
f(x) \:=\: kx^3 - 8x^2 -x +3k + 1,\;k=3$
Why do they do that? . . . Can't they plug in the 3?
. . $\displaystyle \text{and has a zero when }x = 2.$
So we have: .$\displaystyle f(x) \:=\:3x^3 - 8x^2 - x + 10$
Since $\displaystyle f(2) = 0$, then $\displaystyle (x\!-\!2)$ is a factor of $\displaystyle \,f(x).$
We find that: .$\displaystyle f(x) \;=\;(x-2)(3x^2-2x-5) \;=\;(x-2)(x+1)(3x-5)$
Therefore, the zeros are: .$\displaystyle x\:=\:2,\,\text{-}1,\,\frac{5}{3}$
Edit: Too slow . . . again.