Question
or
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
2t3+4t
Answers
GPT-4o mini
To factor out the greatest common factor (GCF) from the polynomial \(2t^3 + 4t\), we first identify the GCF of the coefficients and the variable parts.
1. The coefficients are 2 and 4. The GCF of 2 and 4 is 2.
2. The variable parts involve \(t^3\) and \(t\). The GCF of \(t^3\) and \(t\) is \(t\).
Therefore, the overall GCF of the polynomial \(2t^3 + 4t\) is \(2t\).
Now, we can factor out \(2t\):
\[
2t^3 + 4t = 2t(t^2 + 2)
\]
So, the factored form of the polynomial is:
\[
2t(t^2 + 2)
\]
1. The coefficients are 2 and 4. The GCF of 2 and 4 is 2.
2. The variable parts involve \(t^3\) and \(t\). The GCF of \(t^3\) and \(t\) is \(t\).
Therefore, the overall GCF of the polynomial \(2t^3 + 4t\) is \(2t\).
Now, we can factor out \(2t\):
\[
2t^3 + 4t = 2t(t^2 + 2)
\]
So, the factored form of the polynomial is:
\[
2t(t^2 + 2)
\]