### All SAT Math Resources

## Example Questions

### Example Question #1 : Exponents And The Distributive Property

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 #1 : Exponents And The Distributive Property

x > 0.

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

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

**Possible Answers:**

The relationship cannot be determined from the information given

The two quantities are equal

Quantity A is greater

Quantity B is greater

**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 : Exponents And The Distributive Property

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

Find the product in terms of :

**Possible Answers:**

**Correct answer:**

This question can be solved using the FOIL method. So the first terms are multiplied together:

This gives:

The x-squared is due to the x times x.

The outer terms are then multipled together and added to the value above.

The inner two terms are multipled together to give the next term of the expression.

Finally the last terms are multiplied together.

All of the above terms are added together to give:

Combining like terms gives

.

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

Expand the following expression:

**Possible Answers:**

**Correct answer:**

Expand the following expression:

Let's begin by recalling the meaning of FOIL: First, Outer, Inner, Last.

This means that in a situation such as we are given here, we need to multiply all the terms in a particular way. FOIL makes it easy to remember to multiply each pair of terms.

Let's begin:

First:

Outer:

Inner:

Last:

Now, put it together in standard form to get: