Falak Kinney

2021-02-24

Use the factorization theorem to determine whether $x-\frac{1}{2}$ is a factor
of $f\left(x\right)=2{x}^{4}-{x}^{3}+2x-1$.

pierretteA

Step 1
If $x-\frac{1}{2}$ is a factor then the remainder when f(x) divided by it will be zero.
Put $x-\frac{1}{2}=0$
$x=\frac{1}{2}$
Step 2
Substitute $x=\frac{1}{2}\in f\left(x\right)$.
$f\left(\frac{1}{2}\right)=2{\left(\frac{1}{2}\right)}^{4}-{\left(\frac{1}{2}\right)}^{3}+2\left(\frac{1}{2}\right)-1$
$=\frac{1}{8}-\frac{1}{8}+1-1$
=0+0
=0
Thus the remainder is zero.
$x-\frac{1}{2}$ is a factor of f(x).

Jeffrey Jordon