Factoring by Grouping
Factoring by grouping is a method used to factor quadratic expressions that contain four terms. It involves splitting the four terms into two groups of two terms each, factoring each group, and then finding the common factors between the two factored groups.
In this article, we will discuss some tips for factoring by grouping.
Tips for Factoring by Grouping
- Look for four terms in the quadratic expression. Factoring by grouping works best with quadratic expressions that contain four terms.
- Split the four terms into two groups. The groups should contain two terms each. Make sure the first term in each group has a common factor.
- Factor each group separately. Use any factoring method like taking out the common factor to factor the terms in each group.
- Find common factors between the factored groups. The common factors will give you the final factored form.
- Check your work by multiplying the factors to see if you get the original expression.
Examples of Factoring by Grouping
Factor the expression: x2 + 5x + 6x + 30
Split the 4 terms into 2 groups:
(x2 + 5x) + (6x + 30)
Factor each group:
(x2 + 5x) = x(x + 5)
(6x + 30) = 6(x + 5)
(x2 + 5x) + (6x + 30) = x(x + 5) + 6(x + 5)
The common factor is (x + 5).
The factored form is: (x + 5)(x + 6)
Factor the expression: 3a – 6b + 2a – 4b
Group the terms:
= (3a + 2a) + (-6b – 4b)
= a(3 + 2) – 2b(3 + 2)
= 5a – 2b
Factor the common factor: 5a – 2b
Factor the expression: 4x² – 12xy + 3xz – 9yz
Group the terms:
= (4x² – 12xy) + (3xz – 9yz)
= 4x(x – 3y) + 3z (x – 3y )
= (4x + 3z)(x – 3y)
What type of expressions can be factored by grouping?
Factoring by grouping works for quadratic expressions that contain four terms. The expression must have a common factor between the first terms of each group
Why do we split the expression into two groups of two terms each?
Splitting the four terms into two groups allows us to factor each group separately. Once we factor the groups, we can then find the common factors between them to get the final factored form.
What if I don’t get any common factors when I factor the two groups?
If you don’t get common factors between the groups, then the expression cannot be factored by grouping. You will need to try another factoring method like taking out the greatest common factor