Question

Factor the following polynomial by grouping.

xy + 2y2 + 3x + 6y
OA) (x+y)(2y + 3)
OB) (x+2y)(y + 3)
OC) (x+3y) (y + 2)
OD) (x+y)(3y + 2)

Answer 1

Option B

The factored form by grouping is:

`xy+2y^2+3x+6y = (x+2y)(y+3)`

Solution:

Given that we have to factor the given polynomial by grouping

Given polynomial is:

`xy+2y^2+3x+6y`

Factoring by grouping means that you will group terms with common factors before factoring.

This is done by grouping a pair of terms. Then factor each pair of two terms

In the given polynomial, group the terms that has "x" as common and group the terms that has "y" as common

`(xy+3x)+(2y^2+6y)`

Factor out "x" from first group and factor out "2y" from second group

`x(3+y)+2y(y+3)`

Factor out y + 3

`x(3+y)+2y(y+3) = (x+2y)(y+3)`

Thus the factored form by grouping is:

`xy+2y^2+3x+6y = (x+2y)(y+3)`