Factoring Trinomials with Common Factors Grouping Method.

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Presentation transcript:

Factoring Trinomials with Common Factors Grouping Method

REMEMBER There are many different methods to use when factoring. To be consistent, we will continue to use the factor by grouping method. First, use parentheses to group terms with common factors. Be sure middle sign is + If it is -, change it to +(-) Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same. Before beginning, check for a GCF common to ALL terms, then remove it.

Multiply the first and last terms in the ( ). x 2 (-3) = -3x 2 Check your signs... ‘c’ is – so subtract factors. ‘b’ is – so larger factor will be negative. Replace the middle term with these factors.. Then group. Now, bring down the GCF Switch factors to make middle sign +

Multiply the first and last terms in the ( ). x 2 (-6) = -6x 2 Check your signs... ‘c’ is – so subtract factors. ‘b’ is + so larger factor will be positive. Replace the middle term with these factors.. Then group. Now, bring down the GCF

Multiply the first and last terms in the ( ). 4x 2 (-5y 2 ) = -20x 2 y 2 Check your signs... ‘c’ is – so subtract factors. ‘b’ is + so larger factor will be positive. Replace the middle term with these factors.. Then group. Now, bring down the GCF

Multiply the first and last terms in the ( ). x 2 (-6y 2 ) = -6x 2 y 2 Check your signs... ‘c’ is – so subtract factors. ‘b’ is – so larger factor will be negative. Replace the middle term with these factors.. Then group. Now, bring down the GCF

What is different about this problem? When the leading term is negative, just factor out a negative number to make the leading term positive!!!. Now divide out the negative number!! And, use the grouping method on the trinomial inside the ( ).

What is different about this problem? When the leading term is negative, just factor out a negative number to make the leading term positive!!!. Now divide out the negative number!! And, use the grouping method on the trinomial inside the ( ).

Now divide out the GCF!! And, use the grouping method on the trinomial inside the ( ). None of the factors will SUBTRACT to give +12, so this is as far as you can go.

Now divide out the GCF!! And, use the grouping method on the trinomial inside the ( ). None of the factors will SUBTRACT to give +6, so this is as far as you can go.