The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

First we must FOIL and simplify:

Then we must subtract 23 from both sides.

Then you can choose use the quadratic formula or factor.

If you use the quadratic formula:

     and 

 because x is a positive integer.

If factoring, you must look at the coefficients and signs for for clues

Because -16 and -35 are both negative and 3 is a prime number, we know that the factoring will follow the format

In order to determine what replaces the question marks, we must look at the possible factors for -35 which are: -1 and 35, -35 and 1, 7 and -5, -7 and 5.

Considering -16 is negative AND a fairly low number, I am going to guess that the distribution is:  

It checks out!

Now, set both parts of the equation equal to zero. 

 because x is a positive integer.

Recall the mnemonic FOIL:

When multiplying together two binomials, according to the FOIL method you must find the product of the first terms of both binomials, the product of the terms on the outside of the entire expression, the product of the terms on the inside of the expression, and the product of the last terms of both binomials. The sum of these products is the expanded form of the original expression.

Let us apply the FOIL method to the expression . The first two terms of  are  and . Their product is .

The terms on the outside of the expression  are  and . Their product is .

The terms on the inside of the expression  are  and . Their product is .

The last two terms of  are  and . Their product is .

Adding together each of these products yields

.

Hence, the expanded form of  is .

Use FOIL:

Given

First FOIL the first equation. FOIL means to multiply each term in the first binomial with each term in the second binomial.

Now solve the second equation for .

Substitute the equation for  into the first equation to get a new equation only in terms of .

Distribute to eliminate the parentheses and simplify.

Now use the quadratic formula.

Given a quadratic in the form, 

For this particular question,

From here recall that if the value under the radical sign equals zero than  results in having just one solution.

Therefore, set the value that is under the radical equal to zero and solve for .

Since the binomials containing  are the same, set one equal to zero and solve.

If a problem asks you to expand an expression, you must use the Distributive property. If you are using the FOIL method, you first multiply the first term in each parentheses by each other, followed by the outside terms, then the inside terms, and then the last terms. This is illustrated below. 

First, you multiply  which equals 

Second, you multiply 

Third, you multiply 

Last, you multiply 

Then you simply rearrange them in order of exponents to get 

The problem is basically asking for two binomial expressions to be multiplied and the product to be simplified.

Multiply the two binomials in the definition of the operation using the FOIL method - multiplying each term in the first binomial by each term in the second, as follows:

F(irst): 

O(uter): 

I(nner): 

L(last): 

Add the terms and collect like terms:

The domain means what real number can you plug in that would still make the function work. For this case, we have to worry about the denominator so that it does not equal 0, so we solve the following. 7x – 1 = 0, 7x = 1, x = 1/7, so when x ≠ 1/7 the function will work.