Question

How do you factor and solve `3x^2+6x+3=0`?

Answer 1

`3x^2+6x+3=0`

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 3*3 = 9`
and
`N_1 +N_2 = b = 6`

After trying out a few numbers we get `N_1 = 3` and `N_2 =3`
`3*3 = 9`, and `3+3= 6`

`3x^2+6x+3= 3x^2+3x +3x+3`

`= 3x(x+1) +3(x+1)`

`color(green)((3x+3)(x+1)` is the factorised form.

Answer 2

`x=-1`

Explanation:

Factor a `3` out.

`3(x^2+2x+1)=0`

Realize that the inner portion is a perfect binomial square, equal to `(x+1)^2`.

`3(x+1)^2=0`

Now, to solve for `0`, realize that `(x+1)^2` must equal to `0` in order for the entire expression to be equal to `0`, since `3xx0=0`.

`(x+1)^2=0`
`x+1=0`
`x=-1`

You can check this by graphing the equation. The graph should touch the `x`-axis at `x=-1`.

graph{3x^2+6x+3 [-10.41, 12.09, -2.56, 8.7]}