What does solve by factoring mean

Question

Tell me what this means plz tell me.

Answer 1

Solve by factoring is used to solve equations that have an x² (or higher) term in them.

 

Factoring is when something is broken into pieces that _multiply_ to give the original,

for example 35 is factored as 5 * 7.

So what?

Well, if we can break an equation into pieces that multiply together AND

if those pieces are suppsed to multiply to 0,

then the only way to get 0 is for one (or more) of the pieces to be 0.

 

Simple example:   

   Solve  x² + 5x + 6 = 0

this factors to:   (x + 2) (x + 3) = 0

so for this equation to work (be solved)

we must have either (x + 2) = 0 , or (x + 3) = 0.

So x=-2 or x=-3 will work and they are the solutions of the equation.

 

Note that it is crucial to have the factored parts equal to 0 in order 

to use this method.  Sometimes the equation will need to be expanded,

combined, rearranged so that the right side is 0; then factor it.