I've to solve 3x^2 + 6x +3 =0 by factoring. Thus, after solving I got the answer as 3(x + 1)^2.
Please correct me if I'm wrong.
3x^2 + 6x +3 =0
first divide each term by 3, the fact that the right side is zero and zero divided by anything is zero, we can just drop the 3
x^2 + 2x + 1 = 0
(x+1)^2 =
take √ of both sides
x+1 = 0
x = -1
You had it factored correctly, but you "lost " your equation by dropping the =0 part.
Oh, thanks a lot!
To solve the quadratic equation 3x^2 + 6x + 3 = 0 by factoring, we follow these steps:
Step 1: Set the equation equal to zero:
3x^2 + 6x + 3 = 0
Step 2: Factor out the greatest common factor (GCF) if possible. In this case, the GCF is 3:
3(x^2 + 2x + 1) = 0
Step 3: Attempt to factor the quadratic trinomial inside the parentheses:
x^2 + 2x + 1
This can be factored as (x + 1)(x + 1) or (x + 1)^2
So far, you are correct in factoring the equation as 3(x + 1)^2.
Step 4: Set each factor equal to zero and solve for x:
x + 1 = 0
x = -1
Therefore, the roots of the equation 3x^2 + 6x + 3 = 0 are x = -1 (repeated root).
You have correctly factored the equation, and the answer should be: x = -1 with a multiplicity of 2.