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

Example 1

Factor the expression: x² + 5x + 6x + 30

Solution

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)

Example 2

Factor the expression: 3a – 6b + 2a – 4b

Solution

Group the terms:

= (3a + 2a) + (-6b – 4b)

= a(3 + 2) – 2b(3 + 2)

= 5a – 2b

Factor the common factor: 5a – 2b

Example 3

Factor the expression: 4x² – 12xy + 3xz – 9yz

Solution

Group the terms:

= (4x² – 12xy) + (3xz – 9yz)

= 4x(x – 3y) + 3z (x – 3y )

= (4x + 3z)(x – 3y)

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