Answer:
[tex]3xy^2(-4x^2y^3-3x+4y)[/tex]
Step-by-step explanation:
The given expression is
[tex]-12x^3y^5-9x^2y^2+12xy^3[/tex]
To find the greatest common factor; we find the prime factorization of each term in the expression.
[tex]-12x^3y^5=-2^2\times3\timesx^3\times y^5[/tex]
[tex]-9x^2y^2=-3^2\times x^3 \times y^2[/tex]
[tex]12xy^3=2^2\times 3\times x\times y^3[/tex]
The greatest common factor is the product of the least powers of the common factors.
[tex]GCF=3xy^2[/tex]
We factor the GCF to obtain;
[tex]-12x^3y^5-9x^2y^2+12xy^3=3xy^2(-4x^2y^3-3x+4y)[/tex]
