Question

How do you factor 8x^2+18x+9=0

Answer 1

First off, do a prime factoring of the constant and leading coefficient, namely 9 and 8 respectively.

so a prime factoring of 8 is 2*2*2, and a prime factoring of 9 is 3*3.

so, those are the factors... now, how do we produce products that gives us the middle coefficient +18?

well, let's see  hmmmm 2 * 3 * 3   and 2 * 3....so that's 18 + 6, that's 24.. .so... no good is not 18, let's try again.

2*2*3   and 2 * 3, so that's 12 + 6, now, that's +18

 so we'll use those, 2*2*3 and 2*3, or 4 * 3 an 2 * 3, (4x + 3)(2x + 3) = 0.