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Factoring by Common Factors & by Grouping


In these lessons, we will look at factoring by common factors and factoring of polynomials by grouping.

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Factoring By Common Factors

The first step in factorising is to find and extract the GCF of all the terms.


Factorise the following algebraic expressions:

a) xyz – x2z

b) 6a2b + 4bc


a) xyz – x2z = xz(yx)
b) 6a2b + 4bc = 2b(3a2 + 2c)

Factoring Out The Greatest Common Factor
The following video shows an example of simple factoring or factoring by common factors.
To find the GCF of a Polynomial
1. Write each term in prime factored form
2. Identify the factors common in all terms
3. Factor out the GCF

Factoring Using the Great Common Factor, GCF - Example 1
Two examples of factoring out the greatest common factor to rewrite a polynomial expression.

Factoring Using the Great Common Factor, GCF - Example 2.
Factor out binomial expressions.


Factoring Polynomials with Common Factors
This video provides examples of how to factor polynomials that require factoring out the GCF as the first step. Then other methods are used to completely factor the polynomial.

Factoring By Grouping

When an expression has an even number of terms and there are no common factors for all the terms, we may group the terms into pairs and find the common factor for each pair:


Factorise the following expressions:

a) ax + ay + bx + by

b) 2x + 8y – 3px –12py

c) 3x – 3y + 4ay – 4ax


a) ax + ay + bx + by
= a(x + y) + b(x + y)
= (a + b)(x + y)

b) 2x + 8y – 3px –12py
= 2(x + 4y) –3p(x + 4y)
= (2 – 3p)(x + 4y)

c) 3x – 3y + 4ay – 4ax
= 3(xy) + 4a(yx)
= 3(xy) – 4a(x y)
= (3 – 4a)( x y)

Factoring by Grouping
3 complete examples of solving quadratic equations using factoring by grouping are shown.

Factoring by Grouping - Ex 1.


Factoring By Grouping - Ex 2.

Factoring Trinomials: Factor by Grouping - ex 1.

Factoring Trinomials: Factor by Grouping - ex 2.

The following video gives another example of factoring by grouping.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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