factorin trinomals

Question

10q2+9q+2

need the formula to solve

Answer 1

The two things to look at are the factors of your quadratic (2nd degree term) and the constant term. 

10q² ==> q and 10q, 2q and 5q

2 ==> 1 and 2

Now, which combinations of these, when added together, equal 9q?

q * 1 + 10q * 2 ==> 21q (no)

q * 2 + 10q * 1 ==> 12q (no)

2q * 2 + 5q * 1 ==> 9q (yes)

So our factors would be (2q + 1)(5q + 2)