### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Use Foil

Factor 2x^{2} - 5x – 12

**Possible Answers:**

(x - 4) (2x + 3)

(x + 4) (2x + 3)

(x – 4) (2x – 3)

(x + 4) (2x + 3)

**Correct answer:**

(x - 4) (2x + 3)

Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x^{2} – 5x – 12.

### Example Question #2 : How To Use Foil

x > 0.

Quantity A: (x+3)(x-5)(x)

Quantity B: (x-3)(x-1)(x+3)

**Possible Answers:**

Quantity B is greater

Quantity A is greater

The relationship cannot be determined from the information given

The two quantities are equal

**Correct answer:**

Quantity B is greater

Use FOIL:

(x+3)(x-5)(x) = (x^{2} - 5x + 3x - 15)(x) = x^{3} - 5x^{2} + 3x^{2} - 15x = x^{3} - 2x^{2} - 15x for A.

(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x^{2} + 3x - 3x - 9)(x-1) = (x^{2} - 9)(x-1)

(x^{2} - 9)(x-1) = x^{3} - x^{2} - 9x^{ +} 9 for B.

The difference between A and B:

(x^{3} - 2x^{2} - 15x) - (x^{3} - x^{2} - 9x^{ +} 9) = x^{3} - 2x^{2} - 15x - x^{3} + x^{2} + 9x - 9

= - x^{2} - 4x - 9. Since all of the terms are negative and x > 0:

A - B < 0.

Rearrange A - B < 0:

A < B

### Example Question #3 : How To Use Foil

Solve for all real values of .

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #1 : How To Use Foil

Simplify:

**Possible Answers:**

**Correct answer:**

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:

### Example Question #2 : Exponents And The Distributive Property

Use FOIL to simplify the following product:

**Possible Answers:**

**Correct 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:

### Example Question #3 : Exponents And The Distributive Property

Simplify:

**Possible Answers:**

**Correct answer:**

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:

### Example Question #1 : How To Use Foil With Exponents

If , which of the following could be the value of ?

**Possible Answers:**

**Correct answer:**

Take the square root of both sides.

Add 3 to both sides of each equation.

### Example Question #2 : How To Use Foil With Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

= *x*^{3}*y*^{3}*z*^{3} + *x*^{2}*y* + *x*^{0}*y*^{0} + *x*^{2}*y*

= *x*^{3}*y*^{3}*z*^{3} + *x*^{2}*y* + 1 + *x*^{2}*y*

= *x*^{3}*y*^{3}*z*^{3} + 2*x*^{2}*y* + 1

### Example Question #4 : Exponents And The Distributive Property

**Possible Answers:**

**Correct answer:**

Use the FOIL method to find the product. Remember to add the exponents when multiplying.

First:

Outside:

Inside:

Last:

Add all the terms:

### Example Question #9 : How To Use Foil With Exponents

Square the binomial.

**Possible Answers:**

**Correct answer:**

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

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