How do you factor completely: 6x^2 + 19x + 10?

1 Answer
Nghi N. ยท George C.
Jul 16, 2015

Factor: y = 6x^2 + 19x + 10
y = (3x + 2)(2x + 5)

Explanation:

y = 6x^2 + 19x + 10 = 6(x - p)(x - q).
I use the new AC Method to factor trinomials (Google, Yahoo search)
Converted y' = x^2 + 19x + 60 = (x - p')(x - q'). p' and q' have same sign.
Factor pairs of ac = 60 -> ...(3, 20)(4, 15). This sum is 19 = b.
Then p' = 4 and q' = 15
Then, p = 4/6 = 2/3 and q = 15/6 = 5/2

y = 6(x + 2/3)(x + 5/2) = (3x + 2)(2x + 5)

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