Question

Find the value of $m$ so that $2x-1$ be a factor of $8x^4+4x^3-16x^2+10x+m.$

• A. $-1$
• B. $2$
• C. $-2$
• D. $0$

Answer 1

The correct option is C $-2$

Let $p\left(x\right)=8x^4+4x^3-16x^2+10x+m$ and $g\left(x\right)=2x-1$
Now, $g\left(x\right)=2x-1$
$=>2x-1=0$
$=>x=\frac{1}{2}$
If $g\left(x\right)$ is a factor of $p\left(x\right)$, then $p\left(\frac{1}{2}\right)$ must be $0$
Thus, $p\left(\frac{1}{2}\right)=0$
$=>8(\frac{1}{2}{)}^4+4(\frac{1}{2}{)}^3-16(\frac{1}{2}{)}^2+10(\frac{1}{2})+m=0$
$=>\frac{8}{16}+\frac{4}{8}-\frac{16}{4}+5+m=0$
$=>\frac{1}{2}+\frac{1}{2}-4+5+m=0$
$=>1+1+m=0$
$=>m=-2$