Question

Factor out the greatest common factor from the terms of the polynomial 6x3−12x2+18x (1 point)

Answers

GPT-4o mini
To factor out the greatest common factor (GCF) from the polynomial \(6x^3 - 12x^2 + 18x\), we first need to identify the GCF of the coefficients and the common variable factors.

1. **Identify the GCF of the coefficients (6, -12, and 18)**:
- The GCF of 6, -12, and 18 is 6.

2. **Identify the common variable factor**:
- The lowest power of \(x\) present in all terms is \(x\).

3. **Combine the GCF of the coefficients and the variable factor**:
- The overall GCF is \(6x\).

Now, we can factor out \(6x\) from each term in the polynomial:

\[
6x^3 - 12x^2 + 18x = 6x(x^2 - 2x + 3)
\]

Thus, the factored form of the polynomial is:

\[
6x(x^2 - 2x + 3)
\]

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