Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 387: 16

$R=0$. $x+3$ is a factor

$f\left( x\right) =2x^{6}-18x^{4}+x^{2}-9=\left( x+3\right) q\left( x\right) +R$ $\Rightarrow f\left( -3\right) =2\times \left( -3\right) ^{6}-18\times \left( -3\right) ^{4}+\left( -3\right) ^{2}-9=0=R$ Since $R=0$, $x+3$ is a factor.