How do you factor $10a^2 - 14a - 12$ ?

Question

2013 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-06T13:12:49

$10a^2-14a-12=2(5a^2-7a-6)$

Use AC Method to find factors of $5a^2-7a-6$ ...

$A=5$ , $B=7$ , $C=6$

Look for a pair of factors of $AC=5*6=30$ whose difference is $B=7$ .

The pair $B1=10$ , $B2=3$ works.

Then for each of the pairs $(A, B1)$ , $(A, B2)$ divide by the HCF to get the coefficients of a factor, choosing signs as appropriate:

$(A, B1) = (5, 10) -> (1, 2) -> (a-2)$
$(A, B2) = (5, 3) -> (5, 3) -> (5a+3)$

So:

$10a^2-14a-12=2(5a^2-7a-6) = 2(a-2)(5a+3)$

How do you factor 10a^2 - 14a - 1210a^2 - 14a - 12?