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:

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:

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 .