Question

What is the greatest common factor of the polynomial's terms? 15m2n4−3m3n4+6mn2 Enter your answer in the box.

Answer 1

Answer: 3mn²

Explanation:

`15m^2n^4-3m^3n^4+6mn^2\\\\\\\text{Factor each term:}\\\\15m^2n^4: 3\cdot 5\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n\\\\-3m^3n^4: -1\cdot 3\cdot m\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n\\\\ 6mn^2: 2\cdot 3\cdot m\cdot n\cdot n\\\\\\\\\text{What factors do ALL 3 terms have in common:}`

`\\\\15m^2n^4: \boxed{3}\cdot 5\cdot \boxed{m}\cdot m\cdot \boxed{n\cdot n}\cdot n\cdot n\\\\-3m^3n^4: -1\cdot \boxed{3}\cdot \boxed{m}\cdot m\cdot m\cdot \boxed{n\cdot n}\cdot n\cdot n\\\\ 6mn^2: 2\cdot \boxed{3}\cdot \boxed{m}\cdot \boxed{n\cdot n}\\\\\\\text{They ALL have }3mn^2\text{\ in common. This is the GCF.}`