Question

How to factor the gcf out of a polynomial

Answer 1

Step-by-step explanation:

$15x^6+6x^4+9x^3\\\\\text{Find GCF of 15, 6 and 9:}\\\\15=\boxed3\cdot5\\6=\boxed3\cdot2\\9=\boxed3\cdot3\\\\GCF(15,\ 6,\ 9)=\boxed3\\\\\text{Find GCF of}\ x^6,\ x^4\ \text{and}\ x^3:\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^6=x^{3+3}=\boxed{x^3}\cdot x^3\\\\x^4=x^{3+1}=x^3\cdot x^1=\boxed{x^3}\cdot x\\\\x^3=\boxed{x^3}\cdot1\\\\GCF(x^6,\ x^4,\ x^3)=\boxed{x^3}\\\\\text{Therefore}\\\\GCF(15x^6+6x^4+9x^3)=\boxed{3}\cdot\boxed{x^3}=3x^3\\\\15x^6+6x^4+9x^3=3x^3(5x^3+2x+3)$