Question

How do you factor `2x^{2}+4x-6`?

Answer 1

You cannot (unless you use imaginary numbers, i.e. i).
Maybe check that there is no typo.

Explanation:

The Quadratic Formula: For `ax^2" + bx + c = 0`, the values of x (factors) which are the solutions of the equation are given by:
`x=(b+-sqrt(4*a*c))/(2*a)`

Here, a=2, b=4 and c=-6, so

`x=(4+-sqrt(4*2*(-6)))/(2*2)`

`x=(4+-sqrt(-48)/4)`

since you cannot take the square root of a negative number (-48), there are no real factors of teh equation. this means that, when plotted on a graph, the X-axis is never crossed.

Answer 2

`2(x+3)(x-1)`

Explanation:

`"take out a "color(blue)"common factor "2`

`=2(x^2+2x-3)`

`"the factors of - 3 which sum to + 2 are + 3 and - 1"`

`=2(x+3)(x-1)`