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55n^2-52n+12 (factor it out) stuck

stuck on that one and the following - 

63w^2-89w+30 (factor it out)

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Hi Jill. I did some work to show you the universal method for factorize the trinominal, but it did not go through the right answer is (11n-6)(5n-2)

thank-you!  We understood the concept, but had two problems that we just couldn't figure out.  I have a feeling it was a long day problem....  thanks for the help

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3 Answers

(7w-6)(9w-5);   7x9=63; so try factors of 30:  both are of the same sign (-), since the last term is + and the middle term is (-).  10x3 doesn't work, so 6 and 5 work; 6x9=54 and 5x7=35, adding to 89.

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thank you!  we had worked through all the problems, but for some reason got stuck on these two.  Appreciate it!

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ax2 + bx + c = a(x - x1)(x - x2) , x1 and x2 are roots of equation
ax2 + bx + c = 0 and x1,2 = (-b ± √D)/2a , D = b2 - 4ac 
~~~~~~~~~~~
55n2 - 52n + 12 = 0 , D = 522 - 4 · 55 · 12 = 64
n1 = (52 + 8)/110 = 6/11
n2 = (52 – 8)/110 = 2/5
55(n – 6/11)(n – 2/5) = (11n – 6)(5n – 2)

(11n + 3)(5n + 4)

The key here is recognizing that 55 is the product of two (and two only) primes - 5 and 11. The rest of the problem works itself out