Factor out the GCF of the polynomial15 {x}^(6) {y}^(3) + 10 {x}^(5) {y}^(4) + 5 {x}^(4) {y}^(2)

Question

factor out the GCF of the polynomial
`15 {x}^(6) {y}^(3) + 10 {x}^(5) {y}^(4) + 5 {x}^(4) {y}^(2)`

Answer 1

GCF is the greatest factor that divides the polynomial completely.

The given polynomial is,

`15x^6y^3+10x^5y^4+5x^4y^2`

Expand the polynomial.

`5*3x^4x^2y^2y+5*2x^4^{}xy^2y^2+5x^4y^2`

Take the common factor of the terms outside.

`5x^4y^2(3x^2y+2xy^2+1)`

The common factor outside of the brackest is the GCF.

Therefore, the GCF is,

`5x^4y^2`