SOLUTION: Rewrite the middle term as the sum of two terms and then factor completely. 12{{{w^2}}}+19w+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Rewrite the middle term as the sum of two terms and then factor completely. 12{{{w^2}}}+19w+4      Log On


   

Question 116510: Rewrite the middle term as the sum of two terms and then factor completely.
12w%5E2+19w+4
Answer by jgr45(31) About Me  (Show Source):
You can put this solution on YOUR website!
12w%5E2+19w+4
To factor this we need to find factors of 4 that sum to 19 after multiplying one or both of the factors by 2,3,4,6, or 12. The 9 possibilites are as follows:
(12w+2)(w+2) 24w+2w=26w, no good
(6w+2)(2w+2) 12+4=16, no
(4w+2)(3w+2) 8+6=14, no
(12w+4)(w+1) 12+4=16, no
(6w+4)(2w+1) 6+8=14, no
(4w+4)(3w+1) 4+12=16, no
(12w+1)(w+4) 48+1=49, no
(6w+1)(2w+4) 24+2=26, no
(4w+1)(3w+4) 16+3=19, AHA!!!
So the correct factorization is (4w+1)(3w+4).