Determining the Greatest Common Factor and Factoring by Grouping

Tutoring on Determining the Greatest Common Factor and Factoring by Grouping

Learning Objectives:

Understand to find Greatest Common Factor.

Math Tutoring on Determining the Greatest Common Factor and Factoring by Grouping

Factoring is a technique that is often useful when trying to solve polynomial equations algebraically. The GCF is the largest monomial that divides or is a factor of each term of the polynomial. To factor an expression means to write an equivalent form that is a product. The first step in factoring is always to look for factors common in every term to identify the largest or greatest common factor. Then we use a distributive property to factor out the GCF and write the polynomial as a product. Factor by grouping technique can be useful when there is a binomial factor of a polynomial with four or more terms. To factor by grouping following steps are followed in math tutoring:

1. We divide the polynomial into two groups, the first half, and the second half.

 2. We factor the GCF out of the first half and then factor the GCF out of the second half.

3. We should notice a common binomial or trinomial factor,    depending on how many terms we started with.

4. We factor out the common binomial or trinomial factor.

 

 

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Hook Questions:

1.    What does it mean to factor by grouping?

2.    How do you factor out the GCF from a polynomial?

3.    How do you use the GCF when factoring a 4 term polynomial by grouping?

 

 

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