How do you factor by grouping 20c^2 - 17c - 10?

2 Answers
George C.
May 16, 2015

Have you missed a leading 34c^3 term?

If you have, then we have a simple problem:

34c^3+20c^2-17c-10 = (34c^3+20c^2)-(17c+10)

=2c^2(17c+10)-1(17c+10)

=(2c^2-1)(17c+10)

If the quadratic as given is correct, it does not really group. It only has irrational factors:

20c^2-17c-10

= 20(c-(17-sqrt(689))/40)(c-(17+sqrt(689))/40)

Nghi N.
May 16, 2015

There is another way. I use the new AC Method (Google , Yahoo Search) to factor trinomials.

f(x) = 20x2 - 17x - 10 = (x - p)(x - q)
Converted trinomial: f'(x) = x^2 - 17x + 200 = (x - p')(x - q') with (a.c = 200).
To find p' and q', compose factor pairs of 200. Proceed: (-4, 50)(-5, 40)(-8, 25). This last sum (25 - 8 = 17 = -b) . Then p' = 8 and q' = -25.
We get: p = (p')/a = 8/20 = 2/5, and q = (q')/a = -25/20 = -5/4.

Factored form: f(x) = (x + 2/5)(x - 5/4) = (5x + 2)(4x - 5)

Check by developing.
f(x) = 20x^2 - 25x + 8x - 10 = 20x^2 - 17x - 10. OK

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