If you haven’t read the first tutorial on quadratics and don’t know cross factoring, read it here Factoring Quadratics for idiots. If you still don’t get it, read it again, and remember…

“Mathematics is a game played according to certain simple rules with meaningless marks on paper.” — David Hilbert

So lets start with the meaningless marks!

This example is a bit harder than the last.

Step 1: Start off rewriting the equation again with an X underneath.

Step 2: Next, we’ll work with the first term. What can be multiplied together to get 4x²? 4x and 1x or 2x and 2x . So write each set on the left of the X

Ok, DON’T GIVE UP NOW. This is probably the hardest ( ok, maybe not hard, but long as hell). and remember… this is factoring the easy way, not that stupid way your teacher was trying to teach you as you were doodling.

Step 3: Leave the left side alone and move on to the right side. The ultimate question is What two numbers can i cross multiply to get 12, and when i add them, i get -19 Write out all the possibilities on the side. Starting with the most common factors. 3 and 4, 6 and 2, 12 and 1.

Step 4: We have 5 sets of numbers here. 2 on the left and 3 on the right. Follow this procedure. Cross multiply each set on the right with each set on the left then add the two numbers. Do this until you get -19 as the sum. Take a look

Step 5: So we cross multiplied 3 and 4 with 4x and 1x and got 19…but we need -19! Now for the easy part. If you need the opposite sign, leave the left side alone and change the terms on the right. 4 and 3 must be negative since -4*4 = -16, -3*1= -3, and -16+(-3)= -19

Step 6: Rewrite it from left to right and you get. (4x-3)(x-4) You can check your answer by FOIL.

And there you have it, another tedious factoring problem solved with cross factoring method!
Stay tuned for more easy algebra tutorials!