Factor a quadratic equation to get two binomials I'm wrestling with this quadratic and trying to figure out how to factor it:
$$3x^2 - 5x + 2 = 0$$
I know that the product of the last terms of the binomial for an equation equals the third term of the polynomial. Also, the sum of the products of those two numbers should be the middle (second) term of the polynomial. 
But what two numbers multiply to give $2$ and added together produce $-5$? How do you use the $3$ in this process?

Let me offer a different approach. Try to complete the square, by adding and subtracting suitable terms. $3x^2$ begs for an extra $x^2$ to be added to it, so there we go:
$$
\begin{aligned}
3x^2−5x+2 &= 4x^2 -4x + 1 - x^2 - x + 1 \\
&= (2x-1)^2 -(x^2- 2x+1) - 3x + 2 \\
&= (2x-1)^2 -(x-1)^2 - (3x - 2) \quad \color{red}{\mbox{<-- $a^2-b^2=(a-b)(a+b)$}}\\
&= (2x-1+x-1)(2x-1-x+1) - (3x-2) \\
&= (3x-2)x-(3x-2) \quad \color{red}{\mbox{<-- factor out $(3x-2)$}}\\
&= (3x-2)(x-1)
\end{aligned} 
$$
