Factor by Grouping

How to factor a polynomial by grouping: 2 examples and their solutions.

Example 1

Example

Solution

Split the polynomial into two groups:
a2 - 2a and +5a - 10.

Factor the first group.
a2 - 2a = a(a - 2)

Common Monomial Factor

Factor the second group.
+5a - 10 = +5(a - 2)

So a2 - 2a + 5a - 10 = a(a - 2) + 5(a - 2).

Both groups should have the same factor (a - 2).

Think (a - 2) as a whole and factor it.
Then a(a - 2) + 5(a - 2) = (a + 5)(a - 2).

So (a + 5)(a - 2) is the answer.

Example 2

Example

Solution

Split the polynomial into two groups:
x2 - 4xy and -3x + 12y.

Factor the first group.
x2 - 4xy = x(x - 4y)

Factor the second group.
-3x + 12y = -3(x - 4y)

So x2 - 4xy - 3x + 12y = x(x - 4y) - 3(x - 4y).

Both groups should have the same factor (x - 4y).

Think (x - 4y) as a whole and factor it.
Then x(x - 4y) - 3(x - 4y) = (x - 3)(x - 4y).

So (x - 3)(x - 4y) is the answer.