Question

Using synthetic division determine which of these is a factor of the polynomial $6x^3-19x^2+16x-4$.

• A. $(x-3)$
• B. $(x+3)$
• C. $(x-2)$
• D. $(x+2)$

Answer 1

The correct option is C $(x-2)$

let $f\left(x\right)=6x^3-19x^{2}16x-4$

We generally find the first zero of polynomial by hit and trial method .

Put $x=1$

$f\left(1\right)=6-19+16-4=-1$

So $x=1$ is not the zero of $f\left(x\right)$

Now Put $x=2$

$f\left(2\right)=48-76+32-4=0$

So $x=2$ is a zero of $f\left(x\right)$

$\Rightarrow (x-2)$ is a factor of $f\left(x\right)$

So option $C$ is correct.