Question

Find the GCF (greatest common factor). 18x2y−9x2y2+6x3y18x2y-9x2y2+6x3y

3xy3xy

6x2y6x2y

3x2y3x2y

9xy9xy

3x2y23x2y2

Answer 1

C.
`3x^2y`

Explanation:

Given the trinomial

`18x^2y-9x^2y^2+6x^3y`

consisting of three terms.

Find the greatest common factor of numbers:

`18=2\cdot 3\cdot 3\\ \\9=3\cdot 3\\ \\6=2\cdot 3\\ \\GCF(18,9,6)=3`

Find the greatest common factor of powers x:

`x^2=x\cdot x\\ \\x^3=x\cdot x\cdot x\\ \\GCF(x^2,x^3)=x\cdot x=x^2`

Find the greatest common factor of powers y:

`y=y\\ \\y^2=y\cdot y\\ \\GCF(y,y^2)=y`

Thus, the greatest common factor of the whole terms is

`3\cdot x^2\cdot y=3x^2y`