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?
Best Answer
Here's a procedure that should help:
To factor $ax^2+bx+c$ first find the product of $a \times c$; in this case, $6$
Then you need to find two numbers that multiply to this value, and add up to $b$; pay attention to the signs of both the product and the sum. In this case, the two numbers are $-2$ and $-3$
Now, the only reason to do this is to split the linear term into two parts that will always let you do the following:$$3x^2 - 5x + 2 = 0$$becomes: $$3x^2 - 3x-2x+ 2 = 0$$and now you can factor by grouping, and then take out a common factor$$3x^2 - 3x -2x+ 2 =(3x^2 - 3x)-(2x-2)=3x(x-1)-2(x-1)=(x-1)(3x-2)$$