Question

Factor completely, then place the answer in the proper location on the grid. Write the answer in descending powers of x. 6x 4 + 15x 3 y 2 + 3x 2 y 3

Answer 1

`6 {x}^(4) + 15 {x}^(3) {y}^(2) + 3 {x}^(2) {y}^(3) \\ = {x}^(2) (6 {x}^(2) + 15x {y}^(2) + 3 {y}^(3) ) \\ = {x}^(2) (6 {x}^(2) + {y}^(2) (15x + 3y))`

Answer 2

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

Explanation:

`6{x}^(4)+15 {x}^(3){y}^(2)+3 {x}^(2){y}^(3)`

LEts factor each term

`6x^4= 2*3*x*x*x*x`

`15x^3y^2= 5*3*x*x*x*y*y`

`3x^2y^3= 3*x*x*y*y*y`

GCF is 3x^2

LEts factor out 3x^2

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

The expression is in descending powers of x

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