Solve the Polynomial Equation: x^10 - 16x^6 = 0

To solve the equation $x^{10} - 16x^6 = 0$, follow these steps:

• Step 1: Notice that the common factor in both terms is $x^6$. Factor it out:

$x^6(x^4 - 16) = 0$

• Step 2: Apply the zero product property, which states if a product equals zero, at least one of the factors must be zero.
  Therefore, we have:

$x^6 = 0$ or $x^4 - 16 = 0$

• Step 3: Solve $x^6 = 0$:

The solution to this is $x = 0$.

• Step 4: Solve $x^4 - 16 = 0$:
• Rewrite it as $x^4 = 16$
• Take the fourth root of both sides:

$x = \pm\sqrt[4]{16} = \pm2$

Thus, $x = 2$ or $x = -2$.

Conclusion: The solutions are $x = \pm 2$ and $x = 0$.

Therefore, the correct answer is: Answers a and c