Question

How do you factor `c² - 12cd - 85d²`?

Answer 1

`(c-17d)(c+5d)`

Explanation:

`"using the a-c method"`

`"the factors of - 85 which sum to - 12 are - 17 and + 5"`

`rArrc^2-12cd-85d^2=(c-17d)(c+5d)`

Answer 2

`(c + 5d)(c - 17d)`

Explanation:

`c^2 - 12 cd - 85 d^2 = (c + ad)(c - bd)`

`=> ab = 85, a-b = -12`

`=> a = b - 12`
`=> (b-12)b = 85`
`=> b^2 - 12 b - 85 = 0`
`"disc = "12^2 + 4*85 = 484 = 22^2`
`=> b = (12 pm 22)/2 = 6 pm 11 = -5 or 17`
`=> (a,b) = (-17,-5) or (5,17)`

`=> c^2 - 12 cd - 85 d^2 = (c + 5d)(c - 17d)`