### All College Algebra Resources

## Example Questions

### Example Question #3 : Intermediate Single Variable Algebra

Divide the trinomial below by .

**Possible Answers:**

**Correct answer:**

We can accomplish this division by re-writing the problem as a fraction.

The denominator will distribute, allowing us to address each element separately.

Now we can cancel common factors to find our answer.

### Example Question #1 : Polynomial Functions

Simplify:

**Possible Answers:**

**Correct answer:**

First, factor the numerator of the quotient term by recognizing the difference of squares:

Cancel out the common term from the numerator and denominator:

FOIL (First Outer Inner Last) the first two terms of the equation:

Combine like terms:

### Example Question #1 : Polynomial Functions

Divide:

**Possible Answers:**

**Correct answer:**

First, rewrite this problem so that the missing term is replaced by

Divide the leading coefficients:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat this process with each difference:

, the second term of the quotient

One more time:

, the third term of the quotient

, the remainder

The quotient is and the remainder is ; this can be rewritten as a quotient of

### Example Question #2 : Polynomial Functions

Divide:

**Possible Answers:**

**Correct answer:**

Divide the leading coefficients to get the first term of the quotient:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat these steps with the differences until the difference is an integer. As it turns out, we need to repeat only once:

, the second term of the quotient

, the remainder

Putting it all together, the quotient can be written as .

### Example Question #3 : Polynomial Functions

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

Simplify the following expression:

To begin, we need to recognize the bottom as a difference of squares. Rewrite it as follows.

So our answer is:

### Example Question #4 : Polynomial Functions

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

Simplify the following expression:

First, let's multiply the 3x through:

Next, divide out the x from the bottom:

So our answer is:

### Example Question #4 : Polynomial Functions

**Possible Answers:**

**Correct answer:**

### Example Question #5 : Polynomial Functions

**Possible Answers:**

**Correct answer:**

### Example Question #6 : Polynomial Functions

**Possible Answers:**

**Correct answer:**

### Example Question #8 : Polynomial Functions

**Possible Answers:**

**Correct answer:**