Question
Factor out the greatest common factor from the terms of the polynomial 6x3−12x2+18x
(1 point)
The GCF of the polynomial given is:
(1 point)
The GCF of the polynomial given is:
Answers
GPT-4o mini
To factor out the greatest common factor (GCF) from the polynomial \( 6x^3 - 12x^2 + 18x \), we first identify the coefficients and the variable parts separately.
1. **Coefficients**: The coefficients are 6, -12, and 18. The GCF of these numbers is 6.
2. **Variable parts**: The variable parts are \( x^3 \), \( x^2 \), and \( x \). The GCF of these terms is \( x \), since the lowest power of \( x \) is \( x^1 \).
Now we combine the GCF of the coefficients and the GCF of the variable parts:
- The overall GCF of the polynomial is \( 6x \).
Next, we can factor the GCF out of the polynomial:
\[
6x^3 - 12x^2 + 18x = 6x(x^2 - 2x + 3)
\]
Thus, the GCF of the polynomial \( 6x^3 - 12x^2 + 18x \) is \( 6x \).
1. **Coefficients**: The coefficients are 6, -12, and 18. The GCF of these numbers is 6.
2. **Variable parts**: The variable parts are \( x^3 \), \( x^2 \), and \( x \). The GCF of these terms is \( x \), since the lowest power of \( x \) is \( x^1 \).
Now we combine the GCF of the coefficients and the GCF of the variable parts:
- The overall GCF of the polynomial is \( 6x \).
Next, we can factor the GCF out of the polynomial:
\[
6x^3 - 12x^2 + 18x = 6x(x^2 - 2x + 3)
\]
Thus, the GCF of the polynomial \( 6x^3 - 12x^2 + 18x \) is \( 6x \).