Take, for example, the following quadratic equation: 6x2+13x+6=0
Multiply 6, the leading coefficient, by 6,
the last number in the equation.
6 x 6=36
Find the two numbers that will multiply to 36 and
also add to 13, the middle number.
4 x 9=36 4+9=13
This is the same way the Split Method starts out, but here is where it changes. Now, simply divide each of these numbers by 6, the leading coefficient. 4/6 and 9/6 reduce to 2/3 and 3/2
At this point, rewrite the equation. (x+2/3) (x+3/2)=0
Now find the two possible solutions x= -2/3 and -3/2
To put the equation in its factored form, the fractions must be cleared. Step back to (x+2/3) (x+3/2) +0 and bring each denominator over to its x.
Voila! You have solved for the zeroes of the equation and put it into its factored form.
THE SPLIT METHOD
Take the original equation and perform the same first two steps to come up with the numbers 4 and 9.
Split the middle term of the equation using those two numbers. 6x2+4x+9x+6=0
Factor the equation by grouping. This is where most students become confused. 2x(3x+2) + 3(3x+2)=0
To put the equation in its factored form, add the terms outside the parentheses and place them next to the term that is already in parentheses. (3x+2) (2x+3)=0
Ronit Feldman is a Metro Times editorial intern. E-mail [email protected]