How do you factor #5n^2-4n-1#?

2 Answers
smendyka
Apr 6, 2018

#(5n + 1)(n - 1)#

Nghi N
Apr 6, 2018

(5n + 1)(n - 1)

Explanation:

Use the new AC Method (Socratic, Google Search)
#y = 5n^2 - 4n - 1#
Converted trinomial:
#y' = n^2 - 4n - 5#.
Method. Find the 2 factor numbers of y', then, divide them by a.
Find 2 numbers, that have opposite signs (ac < 0), knowing their sum (b = -4) and their product (ac = - 5). They are 1 and - 5.
Back to y, the factor-numbers are:
#n1 = 1/a = 1/5# and #n2 = -5/5 = -1#
Factored form:
#y = 5(n + 1/5)(n - 1) = (5n + 1)(n - 1)#

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