Question
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
6f3–12f
Questions
6f3–12f
Questions
Answers
GPT-4o mini
To factor out the greatest common factor (GCF) from the polynomial \(6f^3 - 12f\), we first identify the GCF of the coefficients and the variable parts.
1. The coefficients are 6 and -12. The GCF of 6 and -12 is 6.
2. The variable parts are \(f^3\) and \(f\). The GCF of \(f^3\) and \(f\) is \(f\) (since it is the lowest power of \(f\)).
Thus, the GCF of the entire expression \(6f^3 - 12f\) is \(6f\).
Now we can factor it out:
\[
6f^3 - 12f = 6f(f^2 - 2)
\]
So the factored form of the polynomial is:
\[
6f(f^2 - 2)
\]
1. The coefficients are 6 and -12. The GCF of 6 and -12 is 6.
2. The variable parts are \(f^3\) and \(f\). The GCF of \(f^3\) and \(f\) is \(f\) (since it is the lowest power of \(f\)).
Thus, the GCF of the entire expression \(6f^3 - 12f\) is \(6f\).
Now we can factor it out:
\[
6f^3 - 12f = 6f(f^2 - 2)
\]
So the factored form of the polynomial is:
\[
6f(f^2 - 2)
\]