PSAT Math : How to use FOIL
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Example Question #1 : How To Use Foil
Factor 2x2 - 5x – 12
(x - 4) (2x + 3)
(x + 4) (2x + 3)
(x + 4) (2x + 3)
(x – 4) (2x – 3)
(x - 4) (2x + 3)
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Example Question #1 : How To Use Foil
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
The two quantities are equal
Quantity B is greater
Quantity A is greater
The relationship cannot be determined from the information given
Quantity B is greater
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Example Question #1 : Exponents And The Distributive Property
Solve for all real values of 
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an 
Now, we can factor the quadratic in parenthesis. We need two numbers that add to 
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be 
Example Question #1 : Exponents And The Distributive Property
Simplify:
In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:
Next, multiply your first terms together:
Then, multiply your outside terms together:
Then, multiply your inside terms together:
Lastly, multiply your last terms together:
Together, you have
You can combine your like terms, 
Example Question #5 : Exponents And The Distributive Property
Use FOIL to simplify the following product:
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Example Question #6 : Exponents And The Distributive Property
Simplify:
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses: 
Then multiply the outside terms:
Next, multiply the inside terms:
Finally, multiply the last terms:
When you put the pieces together, you have 
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