https://file.aiquickdraw.com/mathbot/file/1729778007293nwgmkhwa.jpg

The problem in the image is to factor the expression:

\[
14x^4 - 6x^3 + 8x^2
\]

We will factor it step by step:

### Step 1: Find the greatest common factor (GCF)
All the terms in the expression contain a factor of \( 2x^2 \), so we can factor that out:

\[
14x^4 - 6x^3 + 8x^2 = 2x^2(7x^2 - 3x + 4)
\]

### Step 2: Check for further factorization
The quadratic inside the parentheses, \( 7x^2 - 3x + 4 \), does not factor further nicely, as it does not have simple roots or factorable terms.

### Conclusion:
The factored form is:

\[
2x^2(7x^2 - 3x + 4)
\]

This matches option **D** in the provided list.

Would you like any further details on this solution?

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Here are 5 related questions you can explore:
1. How can you factor trinomials of different forms?
2. What is the importance of the greatest common factor (GCF) in factoring polynomials?
3. How do you solve quadratic equations when factoring is not possible?
4. What other methods can be used to simplify polynomial expressions?
5. How do you recognize special factoring patterns like perfect squares and differences of squares?

**Tip**: Always check for the greatest common factor (GCF) before attempting any other factoring methods!

Factor the expression 14x^4 - 6x^3 + 8x^2

Learn how to factor the polynomial expression 14x^4 - 6x^3 + 8x^2 step by step. This solution explains factoring out the greatest common factor (GCF) and checking for further factorization, suitable for students in Grades 8-10.

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