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Part 1
Factor out the GCF from the polynomial.
6 x Superscript 6 Baseline minus 4 x squared plus 14 x


Let's solve the problem step by step.

### Given polynomial:
\[
6x^6 - 4x^2 + 14x
\]

### Step 1: Identify the GCF (Greatest Common Factor)
The coefficients are \(6\), \(-4\), and \(14\). The GCF of these numbers is \(2\).
Now, for the variable part:
- The first term has \(x^6\),
- The second term has \(x^2\),
- The third term has \(x\).

The smallest power of \(x\) is \(x\), so the GCF of the variables is \(x\).

Thus, the overall GCF is \(2x\).

### Step 2: Factor out the GCF
Now, factor out \(2x\) from each term:
\[
6x^6 - 4x^2 + 14x = 2x(3x^5 - 2x + 7)
\]

### Final Answer:
\[
2x(3x^5 - 2x + 7)
\]

Would you like further explanation or details on any step?

### Related Questions:
1. How do you find the GCF for polynomials with more terms?
2. How does factoring simplify polynomial equations?
3. What is the importance of factoring in solving equations?
4. How can factoring help in finding roots of a polynomial?
5. What are common errors to avoid when factoring polynomials?

### Tip:
Always check for both numerical and variable factors when identifying the GCF in a polynomial.

Factor out the GCF from the polynomial: 6x^6 - 4x^2 + 14x

Learn how to factor the polynomial 6x^6 - 4x^2 + 14x by finding the Greatest Common Factor (GCF). This step-by-step solution covers essential algebraic concepts for factoring, including identifying the GCF for both numerical coefficients and variable parts. Suitable for students in Grades 8-10.

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