# I am in Algebra and have not had problems solving equations until I started factoring polynomials. Please explain reverse foil method in steps.

pramodpandey | Student

Reverse foil method is the process of changing the form of an expression from one containing terms to factors. A general approach to factoring a trinomial uses the FOIL method in reverse. Its also called as a factoring method. This is also called as foil method binomials.

This method is same as spliting middle term

let  we have binomial of following form

`ax^2+bx+c`  ,`a!=0`

First find  product of a and c i.e

`axxc=ac`

Second  factor ac into rand s i.e

`ac=rxxs`  ,such that

if `ac>0`  then `r+s=b`

if `ac<0 `  then `r-s=b`

Finally

`ax^2+bx+c=ax^2+(r+s)x+c`

`=ax^2+rx+sx+c`

Now taking common and we can factor

e.g

`2x^2+3x+1`

a=2,b=3,c=1

a.c=2.1=2

2=1.1

2+1=3

`2x^2+(2+1)x+1`

`2x^2+2x+x+1`

`2x(x+1)+1(x+1)`

`(x+1)(2x+1)`

F - First, O - Outer, I - Inner and L - Last

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