How do I factor 6y^2 + 17y + 12 by the grouping method?

Question

I have to factor that by the grouping method.

Answer 1

6y² + 17y + 12

The middle term is + 17y

Find the sum of the middle term

multiply the first term 6 times the last term 12 equals 72 and factor

The factors of 72 =

1 x 72
2 x 36
3 x 24
4 x 18
6 x12
8 x 9. . .<.use these factors

+ 8 and + 9 satisry the sum of the middle term

insert + 8y and + 9y into the equation

6x² + 17y + 12

Factor by grouping

6x² + 8y + 9y + 12

2y(3y + 4) + 3(3y + 4)

(2y + 3)(3y + 4)

- - - - - - - - - - s-

Answer 2

6*12 = 72 is the product of the constant and the quadratic term
you need factors of 72 that add to your linear term (17). 8+9 works.

so split the linear term into 8y+9y

6y^2 + 8y + 9y + 12

Group the left and right pairs
(6y^2 + 8y) + (9y + 12)

Factor each pair so there's a common term
2y(3y+4) + 3(3y+4)

Factor out the common 3y+4
(2y+3)(3y+4)

Answer 3

6y^2 + 17y + 12
= 3y(2y + 3) + 4(2y + 3)
= (3y + 4)(2y + 3)

It looks a bit artificial for an expression of that kind, with only one variable.

Answer 4

6*12 = 2*2*2*3*3; 17 = 8+9

(2y + 3)(3y + 4)

Answer 5

i dont noe how to show the work except to do it in my head. there is a formula, but i always write it wrong. but the guys after me r all right tho. gud luck!