Question

Explain the Factor by Grouping method for a trinomial of the form ax²+bx+c where a is a coefficient other than 1

Answer 1

this is the way I'd do it, maybe not the way taught
ax²+bx+c = a(x^2 + (b/a)x + c/a)
find the factors and multiply a into on of them

Answer 2

Example
2x^2 + 4x +2 = 2(x^2 + 2x + 1) = 2(x+1)(x+1)=(2x+2)(x+1)

Answer 3

If ask to solve the quadratic, a well divide out of equation and you get
(x+1)^2