Question

Factor the trinomial
10b^2-27bc-28c^2

Answer 1

10b^2-27bc-28c^2

look at the factors of the coefficients of b^2 and c^2:

10 = (+/-)1, (+/-)2, (+/-)5, (+/-)10
-28 = (+/-)1, (+/-)2, (+/-)4, (+/-)7, (+/-)14

you have nine factors to choose from. but in your mind, you'll have to make an "educated guess" which PRODUCT pair will SUM to -27.

The more practice you do with these... the better you'll get...
Since -27 is "big", it's a good bet we'll have to use the "bigger" coefficients from each:

5 * -7 = -35
2 * 4 = 8

Notice that -35 + 8 = -28. So "let's" try (5b +4c)(2b -7c)... notice this expands to your original trinomial. so this is correct. this is a bit of "guess and check" but as you do more, the better you'll get...