Solve x^2 + 5x + 6 = 0 factor: x^2 + 5x + 6 = (x + 2)(x + 3). How did you get (x+2) and (x+3)?

Question

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Answer 1

One of the wonderful features of algebra (and other math) is the use of letters.  In this problem, x is a variable, and when it has a certain value (the solution), then this equation equals 0.

 

Let's think about the general equation:   (x+a)(x+b) = 0         [these are factors of some equation]

 

What equation?

  Well, use F-O-I-L (First-Outside-Inside-Last):    x² + (b+a)x +ab = 0

 

We are given b+a and ab, and we want to find out what a and b equal.

We are given +5  and +6 and we want to find out what a and b equal.

What two numbers add to 5, but give 6 when multiplied?     How about 2 and 3?

 

So, using FOIL, (x+2)(x+3) = 0

                       x² + 5x + 6 = 0

 

This means that when either factor = 0 the expression equals 0.  This happens when x=-2 and when x=-3.