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Sect. 5.7 Summary of Factoring Techniques

Sect. 5.7 Summary of Factoring Techniques. General Factoring Strategy: Z: ( if needed ) Arrange in Descending Order of Exponents A: ( if needed ) Factor out the Greatest Common Factor B: Count the number of terms remaining:

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Sect. 5.7 Summary of Factoring Techniques

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  1. Sect. 5.7 Summary of Factoring Techniques • General Factoring Strategy: • Z: (if needed) Arrange in Descending Order of Exponents • A: (if needed) Factor out the Greatest Common Factor • B: Count the number of terms remaining: • 2 Terms: If it’s A2-B2 or A3-B3 or A3+B3use the factoring pattern • 3 Terms: If it’s A2+2AB+B2 or A2-2AB+B2 use the factoring pattern If it’s x2+bx+c then use a factors table If it’s ax2+bx+c then use an ac grouping table • 4 Terms: Try grouping terms… 2 and 2, or 3 and 1, or 1 and 3 • >4 Terms: Look for binomial or trinomial patterns, and try grouping • C: Always Factor Completely – did you miss a common factor or is there another pattern to be factored? • D: Check your factorization by multiplying 5.7

  2. Following the Strategy – 1 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Write an equivalent expression by factoring completely: 5.7

  3. Following the Strategy – 2 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  4. Following the Strategy – 3 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  5. Following the Strategy – 4 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  6. Following the Strategy – 5 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  7. Following the Strategy – 6 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  8. Following the Strategy – 7 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  9. Following the Strategy – 8 Clues: Common Factors? Binomials?A2– B2A3+ B3A3– B3 Trinomials?A2+ 2AB + B2A2– 2AB + B2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms?Grouping Factor until Prime Check by Multiplying • Factor: 5.7

  10. What Next? • Section 5.8Applications of Polynomial Equations • Look for patterns … 5.7

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