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FACTORING TRINOMIALS with leading coefficient ax 2 + bx + c to (ax + b)(cx + d)

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1 FACTORING TRINOMIALS with leading coefficient ax 2 + bx + c to (ax + b)(cx + d)

2 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.

3 Using grouping with trinomials Multiply the first and last terms. 21c 2 (-4) =-84c 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. Switch factors to make middle sign +

4 Using grouping with trinomials Multiply the first and last terms. 25y 2 (9) = 225y 2 Check your signs... ‘c’ is + so add factors. ‘b’ is – so both factors will be negative. Replace the middle term with these factors.. Then group. If the first term in the ( ) is negative, You will factor out a negative number.

5 Using grouping with trinomials Multiply the first and last terms. 9x 2 (2) = 18x 2 Check your signs... ‘c’ is + so add factors. ‘b’ is – so both factors will be negative. Replace the middle term with these factors.. Then group. If the first term in the ( ) is negative, You will factor out a negative number.

6 Using grouping with trinomials Multiply the first and last terms. 12x 2 (5) = 60x 2 Check your signs... ‘c’ is + so add factors. ‘b’ is + so both factors will be positive. Replace the middle term with these factors.. Then group.

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9 Using grouping with trinomials Multiply the first and last terms. 4r 2 (7) = 28r 2 Check your signs... ‘c’ is + so add factors. ‘b’ is - so both factors will be negative. None of the factors will ADD to give -1

10 Using grouping with trinomials Multiply the first and last terms. 3x 2 (-5) = -15x 2 Check your signs... ‘c’ is - so subtract factors. ‘b’ is + so larger factor will be positive. None of the factors will SUBTRACT to give +7

11 Solutions to Trinomials Now that we have the factors of each trinomial, we can carry it to the next step and find the SOLUTIONS for each trinomial. Remember to set your factors equal to zero then solve for the variable…. Like this….

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