b) Sum is 29 T 5c2 29cd 6d Rewrite the middle term, 29cd, as 30cd cd. Factor by Product: 5 (6) 30 5c2 29cd 6d 5c(c 6d ) d(c 6d ) Take out the common factor from each group. (c 6d )(5c d ) Factor out (c 6d). Check: (c 6d )(5c d ) 5c2 29cd 6d2 ✓ YOU TRY 4 Factor completely. 2 The integers whose product is 30 and whose sum is 29 are 30 and 1. grouping. 2 5c2 30cd cd 6d 2 a) 2c2 11c 14 b) 6n2 23n 4 c) 8x2 10xy 3y2 EXAMPLE 5 Factor 24w2 54w 15 completely. Solution It is tempting to jump right in and multiply 24 (15) 360 and try to think of two integers with a product of 360 and a sum of 54. Before doing that, ask yourself, “Can I factor out a GCF?” Yes! We can factor out 3. Sum is 18 T 24w2 54w 15 3(8w2 18w 5) Factor out 3. Product: 8 (5) 40 Try to factor 8w2 18w 5 by fi nding two integers whose product is 40 and whose sum is 18. The numbers are 20 and 2. 3(8w2 20w 2w 5) 3 4w(2w 5) 1(2w 5) Take out the common factor from each group. 3(2w 5)(4w 1) Factor out 2w 5. Check by multiplying: 3(2w 5)(4w 1) 3(8w2 18w 5) 24w2 54w 15 ✓ Remember that the best way to read a math book is to write out the examples as you are reading them. YOU TRY 5 Factor completely. a) 20m3 8m2 4m b) 6z2 20z 16 5 Factor ax2 bx c 1a 12 by Trial and Error Earlier, we factored 3x2 10x 8 by grouping. Now we will factor it by trial and error, which is just reversing the process of FOIL. www.mhhe.com/messersmith SECTION 7.2 Factoring Trinomials 371
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