How do you factor #7r ^ { 2} - 41r t - 56t ^ { 2}#?

1 Answer
Nghi N
Oct 30, 2017

(7r + 8t)(r - 7t)

Explanation:

I use the new AC Method to factor trinomial (Google, Socratic Search).
Consider r as variable and t as constant. Factor the trinomial:
#y = 7r^2 - 41tr - 56t^2 =# 7(r + p)(r + q)
Converted trinomial:
#y' = r^2 - 41tr - 392t^2 =# (r + p')(r + q')
Proceed: Find p' and q' of y' then divide them by a = 7.
Find 2 quantities p' and q' knowing the sum (-41t) and the
product (- 392t^2). They 2 are: p' = 8t and q' = - 49t because:
Factor pairs of (- 392t^2) --> ...(4t, - 98t)(8t, - 49t)
So, #p = (p')/a = (8t)/7# and #q = (q')/a = (-49t)/7 = -7t#
Factored form of y:
#y = 7(r + (8t)/7)(r - 7t) = (7r + 8t)(r - 7t)#

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