Question

how to solve the factoring by groupings

Answer 1

\[ax^2 + bx + c\]

find two numbers u and v so that
\[u+v = b\]
\[u \times v = ac\]

\[ax^2 + ux + vx + c\]

and then just take the common factors out *.*

Answer 2

When I am given something such as
\[ax ^{3} + ax^{2} + a + x\],
I 'group' the first two terms, and the last two.
Then factor each of them separately.
The factors that came out of both groups are brought together to form a 3rd group to solve for.

Hint* The degree of the expression should tell you how many answers you should get to solve for. Since this expression's degree is 3, you should look to have 3 groups.

With the three groups, you just set each of them equal to 0 (also known as T-chart)
and solve!

Simple enough. :)