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