HW #2 evens solutions: Check/correct with RED pen. 3a 2b−2ab2 4c2 d 2 −6 z 3 −2z 2 -4 40) p 2 − p−4 R −9 14) 7g 2 h+3g−2h 2 20) a-10 R -6 24) y 2 +9y−28 R 62 26) 2a+ 1 R 9 2 3 3 2 1 1 3 28) g − g + g R 12 2 4 30) 2z5 +4z4 +9z3 +18z2 +33z+66 R 396 12) 16) 22) € Turn in homework with group. (person with the lightest color shirt) Chapter Six Section 6.5 Opener/Notes #3 Work on the “Opener” problems with your group. Opener Solutions: 1) 6ab(4a - 3b) 2) (x - 7)(x + 5) 3) (2x + 3)(x - 7) 4) (x - 7)(x + 7) 5) (a + 1)(a - 2b) 6) (4r - 3)2 Target Goal: • Factor Polynomials (#3 and #4) • Solve Polynomial Equations by Factoring (#5) Factor Completely. Example One: • No GCF • 3 terms (Trial and Error) • make 2 sets of parentheses • split up s2 • try all possibilities for factors of 8 (8*1 and 4*2) • Check by Multiplying. € s2 −6s+8 s s s−8 s−1 Does not check. s−4 s−2 Does check. Final Solution. Factor Completely. Example Two: • Factor out the GCF • 3 terms (Trial and Error) • make 2 sets of parentheses • split up a2 • try all possibilities for factors of 6 (6*1 and 3*2) • Check by Multiplying. € 3a 2 +15a+18 3(a 2 +5a+6) 3a a 3a+6 a+1 Does not check. 3a+2 a+3 Does check. Final Solution. Factor Completely. Example Three: • Factor out the GCF. • 2 terms (Difference of 2 Squares) • Make 2 sets of parentheses. • Split up a2b2. • Split up 121 by finding the square root. • Check by Multiplying.€ 2a 2b 2 −242 2(a 2 b2 −121) 2 ab−11 ab+11 Does check. Final Solution. Factor Completely. • Factor out the GCF. Example Four: • 2 terms (Difference of 2 Cubes) • Make 2 sets of parentheses (1 small and 1 large) • Split up r3 into r and r2. • Split up 8s3 into 2s and 4s2. • Multiply r*2s to get the middle term in large parentheses. € • Check by Multiplying. 2r 3 −16s3 3 3 2(r −8s ) 2( )( 2 2 r−2s r +2rs+4s ) 2 Final Solution. Factor Completely. • No GCF. • 2 terms (Sum of 2 Cubes) • Make 2 sets of parentheses (1 small and 1 large) • Split up a3b3 into ab and a2b2. • Split up 27 into 3 and 9. • Multiply ab*3 to get the middle term in € large parentheses. • Check by Multiplying. Example Five: 3 3 a b +27 ( )( ) 2 2 ab+3 a b −3ab+9 Final Solution. Factor Completely. • No GCF • 3 terms (Trial and Error) • make 2 sets of parentheses • split up x4 • try all possibilities for factors of 36 (36*1, 18*2, 12*3, 9*4, and 6*6) • Continuing factoring the difference of 2 squares. • Check by Multiplying. € Example Six: 2 4 x −13x +36 x 2 2 x 2 2 x x−3 x+3 x−2 x+2 -9 x -4 Factor Completely. • No GCF • 4 terms (Grouping) • Factor out 4a from the 1st 2 terms. • Factor out 1 from the 2nd 2 terms. • Factor out (5x - 2) from the 2 remaining € terms. Example Seven: 20ax−8a+5x−2 4a(5x−2)+1(5x−2) (5x−2)(4a+1) Factor Completely. • No GCF • 4 terms (Grouping) • Factor out 2x2 from the 1st 2 terms. • Factor out -25 from the 2nd 2 terms. • Factor out (2a+3) from the 2 remaining terms. • Continue by factoring the difference of 2 € squares. Example Eight: 2ax 2 +3x 2 −50a−75 x 2 2a+3 −25(2a+3) (2a+3)(x 2 −25) (2a+3)(x−5)(x+5) Note: If you can’t factor “Prime” Target Goal: • Factor Polynomials (#3 and #4) • Solve Polynomial Equations by Factoring (#5) Homework #3 Worksheet See board for ch.6 test date
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