what does FOIL mean and when do we use it?

Question

what does FOIL mean and when do we use it?

Answer 1

FOIL stands for First, Outer, Inner, Last

 

Lets say for instance you have the following situation:

 

(x-2)*(x+3)

 

In order to perform this operation we need to use the foil method:

 

1. First - Multiply the first terms in each expression:      x * x = x^2

2. Outer - Multiply the outer terms in each expression:   x * 3 = 3x

3. Inner - Multiply the inner terms in each expression:   -2 * x = -2x

4. Last - Multiply the last terms in each expression:   -2 * 3 = -6

 

When we put these into one equation we get the following:

 

x^2 +3x - 2x - 6

 

This reduces down to: x^2 + x - 6

 

When we factor this expression we get the following:  (x+2) * (x-3)  which is what we started with before.

 

Factoring allows us to find the roots of a polynomial more easily.  While FOILing allows you to move from the roots back to the polynomial expression.