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4.3B: Factoring – Dividing out a Common M onomial

4.3B: Factoring – Dividing out a Common M onomial. ALWAYS try to do this FIRST if possible Divide ALL terms by the same thing LARGEST number possible SMALLEST power of a variable existing in all terms Put what you divide by (common monomial) out front

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4.3B: Factoring – Dividing out a Common M onomial

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  1. 4.3B: Factoring – Dividing out a Common Monomial • ALWAYS try to do this FIRST if possible • Divide ALL terms by the same thing • LARGEST number possible • SMALLEST power of a variable existing in all terms • Put what you divide by (common monomial) out front • Result after you divide goes in the ( ) • Factor more if possible • Difference of 2 squares • Perfect Square Trinomial • Etc.

  2. Examples • Divide out a common monomial factor • 1. 2x – 12 • 2. 4x² - 16x • 3. + 12 • 4. 2x²z³ + 4xyz² - 8yz

  3. Solving: (find zeros, roots, x-intercepts) • After dividing out common monomial factor • Set ALL factors =0 and solve • Each ( ) is a factor • Common monomial (what you divided by and put out front) is also a factor • If the monomial doesn’t have a variable, it is only a coefficient (not a factor), so no solution comes from it. ( # ≠ 0)

  4. Examples: Factor and Solve • 5. 2x² + 24x + 72 • 6. 4x³ + 48x² + 144x • 7. 3 + 36x³ + 108x² • 8. x² - 3x

  5. More Examples: Factor and Solve • 9. x² + 5x • 10. 2 - 72x • 11. 3x² - 18x + 27 • 12. x² = 10x

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