Think of the equation in this format to help with the following explanation. We then notice that all four numbers are divisible by four, so we can simplify the expression to. To do this we subtract 128 from both sides to get. 2 × -2 = 4, so we can see that the factored terms in parentheses multiply to become the original equation.This is a factoring problem, so we need to get all of the variables on one side and set the equation equal to zero. In this case, adding a -2 to both blank spaces gives the correct answer. However, once we realize that 3 only has two factors (3 and 1), it becomes easier, because we know that our answer must be in the form (3x +/- _)(x +/- _). 3x 2 - 8x + 4 at first seems intimidating. If both are 1, you've essentially used the shortcut described above. Either d or e (or both) can be the number 1, though this is not necessarily so. If the equation is in the form ax 2+bx+c and a>1, your factored answer will be in the form (dx +/- _)(ex +/- _), where d and e are nonzero numerical constants that multiply to make a. This is also known as factoring by inspection. Believe it or not, for uncomplicated quadratic equations, one of the accepted means of factoring is simply to examine the problem, then just consider possible answers until you find the right one.
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