Factor completely, then place the factors in the proper location on the grid.

3y 2 + 7y + 4

So the factors are (y + 1) (y + 4/3)

Step-by-step explanation:

Given in the question an equation

3y² + 7y + 4

To find it's factor we will use quadratic formula

y = - b ± √ (b²-4 (a) (c)) / 2a

here a = 3

b = 7

c = 4

y1 = - 7 + √ (7² - 4 (3) (4)) / 2 (3)

= - 7 + √49 - 48 / 6

= - 7 + 1 / 6

= - 6/6

= - 1

y2 = - 7 - √ (7² - 4 (3) (4)) / 2 (3)

= - 7 - √49 - 48 / 6

= - 7 - 1 / 6

= - 8/6

= - 4/3

So the factors are (y + 1) and (y + 4/3)

(3y + 4) (y + 1)

Step-by-step explanation:

3y^2 + 7y + 4

a = 3, b = 7 and c = 4

ac = 3 x 4 = 12

The products of 12 = 3 and 4 and sum of 3 and 4 = 7

So

3y^2 + 7y + 4

= 3y^2 + 3y + 4y + 4

= 3y (y + 1) + 4 (y + 1)

= (3y + 4) (y + 1)

Answer

(3y + 4) (y + 1)