STEP 1: Draw a 2 x 2 box. In the upper left box, put the first term, 2x^2 . In the lower right box, put the last term, -3.

STEP 2: Now multiply 2* -3, and list the factors of this product. 2*-3 = -6. The factors of -6 are:

-1 and 6,

1 and -6,

-2 and 3,

2 and -3

STEP 3; Add all the factors. Which factors add up to the "b" value of the polynomial (-5)? In this case, 1 and -6 add up to -5. We put these values, as coefficients of x, in the other boxes (does not matter which factor goes in which remaining box).

STEP 4: Now we factor the columns and rows, putting the greatest common factors outside each row and column of the box.

STEP 5: The factored values represent the values of the bionomial factors. In this case we get (2x + 1) and (x - 3) as our binomial factors.

STEP 6: Check by multiplying these factors, verifying we get the original polynomial as a product. In this case, (2x + 1)(x - 3) = 2x^2 -5x - 3, which is what we started with.