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Divide and Conquer: Factoring x2+bx+c

Divide and Conquer: Factoring x2+bx+c

Author: Nate Muckley
Description:

Learn about factoring expressions in the form of x2 + bx + c. It's fun I swear.

Descriptions, a video, and some fun pictures will teach you all about factoring expressions in the form of x2+bx+c. The x2 is x squared, but I am unable to write exponents in the summary or title.

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Tutorial

Welcome!

     FACTORING is splitting a number of expression into smaller parts.  Those parts multiply together to equal the original number.

For example:

6

can be made with 2 x 3 or 6 x 1

Therefore, factors of 6 are 2 & 3 and 6 & 1

     Factors can be taken from expressions too.  It's a bit trickier, but not impossible.  This packet will show you how to factor expressions in the form of x2 + bx + c.

     Factoring is just like dividing a section into smaller parts, so it is easier to conquer!

    

     Some things to know before going forward: FOIL-ing is the method of multiplying two binomials, First Outer Inner Last.  Check out this awesome packet if you need to jog your memory.  And in the next video, when I refer to "the last video," I mean this description.

Factoring Trinomials!

Learn how to factor trinomials in the form of x2+bx+c. Feel free to turn off the sound, I just put the music in for fun.

Tips for Positive & Negative.

Factors for the numbers change when either b or c are negative in the equation:


x2 + bx + c


Purplemath.com writer Elizabeth Stapel provides tips for deciding whether the factors will be positive or negative:


  • If c is positive, then the factors you're looking for are either both positive or else both negative.
    If b is positive, then the factors are positive
    If b is negative, then the factors are negative.
    In either case, you're looking for factors that add to b.

  • If c is negative, then the factors you're looking for are of alternating signs;
    that is, one is negative and one is positive.
    If b is positive, then the larger factor is positive.
    If b is negative, then the larger factor is negative.
    In either case, you're looking for factors that are b units apart.

  

 

Source: Stapel, Elizabeth. "Factoring Quadratics: The Simple Case." Purplemath. Available from http://www.purplemath.com/modules/factquad.htm. Accessed 25 June 2010

Solve by Factoring

Solving Example 2