2-factoring-quadratics-how-mathbff

MIT grad shows how to factor quadratic expressions. If you want to skip to the shortcut method, jump to 5:06. More videos with Nancy coming in 2017!

The shortcut method ("The Magic X") helps you factor any tough quadratic that doesn't begin with x^2 but instead begins with 2x^2 or 3x^2, or 4x^2, etc.

1) IF YOUR QUADRATIC STARTS WITH X^2: It is faster to use the normal method for factoring in this case: trial and error. Say you have x^2 + 4x - 12. You need to find two numbers that multiply to the last number, -12, AND that add to the second coefficient, positive 4. First make a list of all pairs of numbers that multiply to -12. Then check which pair also adds to positive 4. Use the two numbers in this pair to write your factors.

2) IF YOUR QUADRATIC STARTS WITH 2X^2 OR 3X^2 OR 4X^2, ETC:

A) First check whether your leading coefficient (2 or 3 or 4, etc) is just an overall constant that you can factor out of every term in the quadratic. If it is, factor it out first and then use Method #1 above to factor the X^2 expression that remains.

B) If your leading coefficient cannot be factored out evenly from every term, it will be faster and easier to use the shortcut "magic X" method instead of Method #1. See this method explained at time 5:06 in this video.

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