Factor the trinomial 6y^2+19y+15?

6y^2+43

Step-by-step explanation:

6y^2+(19+15)

(2y+3)(3y+5)

Step-by-step explanation:

6y^2+19y+15

Factor the expression by grouping. First, the expression needs to be rewritten as 6y^2+ay+by+15. To find a and b, set up a system to be solved.

a+b=19

ab=6×15=90

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 90.

1,90

2,45

3,30

5,18

6,15

9,10

Calculate the sum for each pair.

1+90=91

2+45=47

3+30=33

5+18=23

6+15=21

9+10=19

The solution is the pair that gives sum 19.

a=9

b=10

Rewrite 6y^2+19y+15 as (6y^2+9y)+(10y+15).

(6y^2+9y)+(10y+15)

Factor out 3y in the first and 5 in the second group.

3y(2y+3)+5(2y+3)

Factor out common term 2y+3 by using distributive property.

(2y+3)(3y+5)