How to use FOIL - PSAT Math

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

First, move all terms to one side of the equation to set them equal to zero.

All terms contain an , so we can factor it out of the equation.

Now, we can factor the quadratic in parenthesis. We need two numbers that add to and multiply 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 .

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, , to give you the final answer:

Use the FOIL method (first, outside, inside, last) to find the product of:

First:

Outside:

Inside:

Last:

Sum the products to find the polynomial:

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 . Notice that the middle terms cancel each other out, and you are left with . When you distribute the two, you reach the answer: