110113 Factoring

# 5 4 x 7 using a multiplication table name honors

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– 5) · (–4 x + 7) using a multiplication table.

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Name Honors Algebra 2 December 14, 2011 notes and homework page 2 Factoring using a multiplication table Performing the distributive property in the reverse direction is called factoring . Typically factoring is harder than distributing, because often not obvious how to reverse the final step in which the like terms are combined. For example, to factor a quadratic function, you usually have to find the correct way to split up the bx term so that a multiplication table can be completed. Example: Factor 2 x 2 – 5 x – 12. Certain parts of the multiplication table can be filled in right away: x ? 2 x x 2 ? –12 The remaining inside cells need to be filled by two linear terms that will add up to –5 x and lead to completely valid multiplication table. These cells can be found either by trial-and-error, or by a more systematic method taught on the next page. For this example, here are a few of the various possibilities that could be considered: x ? 2 x x 2 x ? –6 x –12 x ? 2 x x 2 x ? –4 x –12 x ? 2 x x 2 3 x ? –8 x –12 x ? 2 x x 2 –8 x ? 3 x –12 The last possibility is the one that works, for now the table can be completed in this way: x –4 2 x x 2 –8 x 3 3 x –12 giving the factorization 2 x 2 – 5 x – 12 = ( x – 4)(2 x + 3). You try it: Factor these quadratics using a multiplication table with a trial-and-error approach. a. Factor 4 x 2 + 13 x + 10. ? ? ? ? b. Factor 6 x 2 – 23 x + 20. ? ? ? ?
Name Honors Algebra 2 December 14, 2011 notes and homework page 3 A systematic approach to factoring What kind of adding and multiplying relationship is present in a multiplication table for ax 2 + bx + c ? Let’s look at the solutions to the last two problems, and look for a pattern.

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