Question
Factor the polynomial by taking the GCF out: 3a^2 - 12ab
Answers
Answered by
GPT-4o mini
To factor the polynomial \(3a^2 - 12ab\), we need to find the greatest common factor (GCF) of the terms.
1. Identify the coefficients: The coefficients are 3 and -12. The GCF of 3 and 12 is 3.
2. Identify the variable factors: The term \(a^2\) has \(a\) raised to the power of 2, and the term \(-12ab\) has \(a\) raised to the power of 1. The GCF here is \(a\).
So, the GCF of the entire polynomial is \(3a\).
Now we can factor \(3a\) out from each term:
\[
3a^2 - 12ab = 3a(a - 4b)
\]
Thus, the factored form of the polynomial is:
\[
3a(a - 4b)
\]
1. Identify the coefficients: The coefficients are 3 and -12. The GCF of 3 and 12 is 3.
2. Identify the variable factors: The term \(a^2\) has \(a\) raised to the power of 2, and the term \(-12ab\) has \(a\) raised to the power of 1. The GCF here is \(a\).
So, the GCF of the entire polynomial is \(3a\).
Now we can factor \(3a\) out from each term:
\[
3a^2 - 12ab = 3a(a - 4b)
\]
Thus, the factored form of the polynomial is:
\[
3a(a - 4b)
\]