Factor completely. If a polynomial cannot be​ factored, say it is prime.
10x Superscript 6minus10x squared

The given polynomial is:

\[ 10x^6 - 10x^2 \]

To factor this polynomial, we first look for the greatest common factor (GCF).

### Step 1: Factor out the GCF

The GCF of the terms \( 10x^6 \) and \( 10x^2 \) is \( 10x^2 \). Factoring out \( 10x^2 \), we get:

\[
10x^2(x^4 - 1)
\]

### Step 2: Factor the difference of squares

Notice that \( x^4 - 1 \) is a difference of squares. It can be factored further:

\[
x^4 - 1 = (x^2 - 1)(x^2 + 1)
\]

### Step 3: Factor the difference of squares again

The expression \( x^2 - 1 \) is also a difference of squares:

\[
x^2 - 1 = (x - 1)(x + 1)
\]

Thus, the completely factored form of the polynomial is:

\[
10x^2(x - 1)(x + 1)(x^2 + 1)
\]

### Final Answer:
The polynomial \( 10x^6 - 10x^2 \) factors completely as:

\[
10x^2(x - 1)(x + 1)(x^2 + 1)
\]

This is fully factored, and it cannot be factored further.

Would you like more details or have any questions?

### Relative Questions:
1. How do you factor a polynomial using the difference of squares?
2. What is the process of finding the greatest common factor in a polynomial?
3. How can you determine if a polynomial is prime?
4. How do you factor trinomials?
5. What are the steps to factor polynomials with higher powers?

### Tip:
Always check for the greatest common factor first before attempting to factor more complex expressions.

Learn how to factor the polynomial 10x^6 - 10x^2 step-by-step with detailed explanations. This problem involves polynomial factoring and the difference of squares method. Suitable for high school students.

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