Falak Kinney

2021-02-24

Use the factorization theorem to determine whether $x-\frac{1}{2}$ is a factor

of$f\left(x\right)=2{x}^{4}-{x}^{3}+2x-1$ .

of

pierretteA

Skilled2021-02-25Added 102 answers

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).

If

Put

Step 2

Substitute

=0+0

=0

Thus the remainder is zero.

Jeffrey Jordon

Expert2021-11-14Added 2605 answers

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