Question

factor 3x^2+8x+4=0

Answer 1

i dont understand?

Answer 2

This is what you would call a harder trinomial. To factorise it, we need to do something about the 3 on the x² term. The easiest way to deal with it is to multiply it with the constant.
Now, 3×4 is 12, so we need to find two numbers that, when we add them, we get 8, but when we multiply them, we get 12. 2 and 6 will do nicely (2+6=8, 2×6=12).
Now, we split our 8x term into 2x+6x, which gives us the expression:
3x² + 6x + 2x + 4 = 0
Now, we need to factorise each half of our expression. The common factor in 3x² + 6x is 3x, so we factor it out and get 3x(x+2). The common factor in 2x + 4 is 2, so we factor it out and get 2(x+2). So now we have:
3x(x+2) + 2(x+2) = 0
We have a common factor of (x+2), so we factor it out and we're left with:
(3x+2)(x+2) = 0,
which is our final answer.