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.