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Factoring Quadratics: Grouping

Factoring Quadratics: Grouping. The method of Grouping for factoring is used when the quadratic has 4 or more terms where a group of them share a Common Factor but not all terms share this Common Factor. . (1) Look for the groups of terms that share a Common Factor and group these, if needed. .

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Factoring Quadratics: Grouping

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  1. Factoring Quadratics:Grouping

  2. The method of Grouping for factoring is used when the quadratic has 4 or more terms where a group of them share a Common Factor but not all terms share this Common Factor.

  3. (1) Look for the groups of terms that share a Common Factor and group these, if needed. To factor using Grouping:

  4. The terms are already grouped correctly here, as the first two terms have a Common Factor (x) and the last two terms have a different Common Factor (−5). (2) Underline the groups to be factored to help focus on each group separately.

  5. (3) Factor each underlined group.

  6. (4) Remove the bracketed Common Factor to complete the factoring.

  7. The factoring is complete.

  8. Example 1: Factor fully using Grouping.

  9. Solution: (1) Look for the groups of terms that share a Common Factor and group these, if needed.

  10. Solution: Groups are fine as given. (2) Underline the groups to be factored to help focus on each group separately.

  11. Solution: (3) Factor each underlined group.

  12. Solution: (4) Remove the bracketed Common Factor to complete the factoring.

  13. Solution: The factoring is complete.

  14. Now try part b).

  15. Solution: • Look for the groups of terms that share a Common Factor and group these, if needed. • Underline the groups to be factored to help focus on each group separately. • Factor each underlined group. • Remove the bracketed Common Factor to complete the factoring.

  16. Solution: Here’s a solution.

  17. It’s time to try part c).

  18. Solution: Follow the steps outlined in the previous slides, noting there is a Common Factor that should be removed first.

  19. Solution: Here’s a solution.

  20. Solution: Here’s an alternate solution, if the common factor is NOT removed first.

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