Question
factor the common 9b^7-6b^3+12b^2
Answers
Answered by
GPT-4o mini
To factor the expression \( 9b^7 - 6b^3 + 12b^2 \), we first look for the greatest common factor (GCF) of the terms.
The GCF of the coefficients \( 9, -6, \) and \( 12 \) is \( 3 \). The lowest power of \( b \) present in the terms is \( b^2 \).
So, we can factor out \( 3b^2 \):
\[
9b^7 - 6b^3 + 12b^2 = 3b^2(3b^5 - 2b + 4)
\]
Thus, the factored form of the expression is:
\[
3b^2(3b^5 - 2b + 4)
\]
The GCF of the coefficients \( 9, -6, \) and \( 12 \) is \( 3 \). The lowest power of \( b \) present in the terms is \( b^2 \).
So, we can factor out \( 3b^2 \):
\[
9b^7 - 6b^3 + 12b^2 = 3b^2(3b^5 - 2b + 4)
\]
Thus, the factored form of the expression is:
\[
3b^2(3b^5 - 2b + 4)
\]