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 A 2 -B 2 or A 3 -B 3 or A 3 +B 3 use the factoring pattern  3 Terms: If it’s A 2 +2AB+B 2 or A 2 -2AB+B 2 use the factoring pattern If it’s x 2 +bx+c then use a factors table If it’s ax 2 +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 5.71

Following the Strategy – 1  Write an equivalent expression by factoring completely: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.72

Following the Strategy – 2  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.73

Following the Strategy – 3  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.74

Following the Strategy – 4  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.75

Following the Strategy – 5  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.76

Following the Strategy – 6  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.77

Following the Strategy – 7  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.78

Following the Strategy – 8  Factor: Clues: Common Factors? Binomials? A 2 – B 2 A 3 + B 3 A 3 – B 3 Trinomials? A 2 + 2AB + B 2 A 2 – 2AB + B 2 a=1, use a Factors table a≠1, use an ac Group table 4 or More Terms? Grouping Factor until Prime Check by Multiplying 5.79

What Next?  Section 5.8 Applications of Polynomial Equations Section 5.8  Look for patterns … 5.710