In any quadratic expression :
![ax^2+bx+c](https://img.qammunity.org/2023/formulas/mathematics/high-school/knmog89o03f8dx9fluvbqb64q9rt61y6kp.png)
We can factor it by :
![(ax^2+mx)+(nx+c)](https://img.qammunity.org/2023/formulas/mathematics/college/smgpx5yflkn3bf2w1lmvtweib3zdvqeesc.png)
where m and n can be obtained using the ac method.
m and n are the factors of the product of a and c which has a sum of b
From the problem, we have :
![3x^2+5x+4](https://img.qammunity.org/2023/formulas/mathematics/college/k54wq3ba1vx0rlj1i7u5xug2k21oh5nkpz.png)
a = 3, b = 5 and c = 4
The product of a and c is 3 x 4 = 12
We need to think of factors of 12 which has a sum of b = 5 for m and n.
The factors of 12 are :
1 x 12
2 x 6
3 x 4
and the sum of any pair is NOT equal to 5.
Therefore, the given quadratic expression is NOT Factorable
ANSWER :
Not factorable