Question

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

3y 2 +7y + 4

Answer 1

(3y + 4)(y + 1)

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)

Answer 2

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

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)