Factoring by Grouping (Part 1)

Factoring by Grouping (Part 1)

How to factor a polynomial by grouping (part 1): examples and their solutions.

Example 1

Factor the given polynomial. a^2 - 2a + 5a - 10

Factor the first two terms:
a2 - 2a = a(a - 2).

Factor the next two terms
with making the (a - 2) factor:
+5a - 10 = +5(a - 2).

The GCF is (a - 2).

So, by factoring,
a(a - 2) + 5(a - 2) = (a + 5)(a - 2).

Example 2

Factor the given polynomial. x^2 - 4xy - 3x + 12y

Factor the first two terms:
x2 - 4xy = x(x - 4y).

Factor the next two terms
with making the (x - 4y) factor:
-3x + 12y = -3(x - 4y).

The GCF is (x - 4y).

So, by factoring,
x(x - 4y) - 3(x - 4y) = (x - 3)(x - 4y).