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FACTORING TRINOMIALS with leading coefficient

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

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FACTORING TRINOMIALS with leading coefficient

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  1. FACTORING TRINOMIALSwith leading coefficient ax2 + 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. Multiply the first and last terms. 21c2(-4) =-84c2 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. Using grouping with trinomials Switch factors to make middle sign + Factors of -84 (larger is - ) Difference of factors = -5

  4. Multiply the first and last terms. • 25y2(9) = 225y2 • 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. Using grouping with trinomials Factors of 225 (both are - ) Sum of factors = -30 If the first term in the ( ) is negative, You will factor out a negative number.

  5. Multiply the first and last terms. • 9x2(2) = 18x2 • 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. Using grouping with trinomials Factors of 18 (both are - ) Sum of factors = -9 If the first term in the ( ) is negative, You will factor out a negative number.

  6. Multiply the first and last terms. • 12x2(5) = 60x2 • 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. Using grouping with trinomials Sum of factors = +19 Factors of 60 (both are + )

  7. What's different here? It's out of order... Put in descending order first!! Now follow the same steps! Sum of factors = +33 Factors of 200 (both are + )

  8. What's different here? It's out of order... Put in descending order first!! Now follow the same steps! Difference of factors = +3 Factors of -40 (larger is + )

  9. Multiply the first and last terms. • 4r2(7) = 28r2 • 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 Using grouping with trinomials Sum of factors = -1 Factors of 28 (both are - )

  10. Multiply the first and last terms. • 3x2(-5) = -15x2 • 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 Using grouping with trinomials Difference of factors = +7 Factors of -15 (larger is + )

  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….

  12. The roots (solutions) are -1/3 and 4/7

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