What is factoring by grouping?

Answer 1

Identifying Polynomials, and factoring them by grouping terms.

For Example:
Factor: 5(x+y) +w(x+y) You see you can group x+y

So it equals (x+y)(5+w) After, you group the reamaning terms.

Answer 2

Factoring by grouping is similar to grouping like terms in regular algebra.

For instance, if you have

x^2 (x + 2) - 4 (x + 2)

Then, as you can notice, we have (x + 2) in both terms. That means we can effectively "factor" out (x + 2), as if it were something like y. After all, if

(x^2)(y) - 4(y) can become
y(x^2 - 4)

Why can't

x^2 (x + 2) - 4 (x + 2) become
(x + 2) (x^2 - 4)?

That's the whole concept of grouping.

An example of when you'd have to group is here:

Factor x^3 - 4x^2 + 2x - 8.

Factor the first two terms and the second two terms.

x^2 (x - 4) + 2(x - 4)

Now, group.

(x^2 + 2) (x - 4)

Answer 3

it mean collecting similar variables into groups for example
ab+cb+xa+xc
to factorize the above by grouping, we collect similar variable into groups as seen below;
b(a+c)+x(a+c)

that's it

Answer 4

identlfying patterns