### All Algebra 1 Resources

## Example Questions

### Example Question #1 : How To Divide Polynomials

Simplify

**Possible Answers:**

**Correct answer:**

When dividing exponents, you subtract exponents that share the same base, so

and and .

Do not forget to "add the opposite" when subtracting negative numbers).

Now, you have

But you are not done yet! Remember, you do not want to have a negative exponent, and the way to turn the negative exponent into a positive exponent is to take its reciprocal, like this:

You keep the rest of the equation in the numerator, leaving you with

### Example Question #2 : Polynomial Operations

Simplify the rational expression.

**Possible Answers:**

**Correct answer:**

To simplify, we must use exponent rules. For exponents in fractions, we can subtract the exponent of the denominator from the exponent in the numerator.

With this rule, we can rewrite the problem.

Remember that negative exponents get moved back to the denominator, turning them positive.

### Example Question #3 : Polynomial Operations

Find the Greatest Common Factor (GCF) of the following polynomial:

**Possible Answers:**

**Correct answer:**

4 goes into 24, 12, 8, and 4.

Similarly, the smallest exponent of x in the four terms is 2, and the smallest exponent of y in the four terms is 1.

Hence the GCF must be .

### Example Question #4 : Polynomial Operations

Divide:

**Possible Answers:**

**Correct answer:**

Divide each of the terms in the numerator by the denominator:

Simplify each term above to get the final:

### Example Question #5 : Polynomial Operations

Find the quotient:

**Possible Answers:**

**Correct answer:**

The numerator can be factored into

,

which when divided by ,

gives us .

Alternate method: Long division of the numerator by the denominator gives the same answer.

### Example Question #6 : Polynomial Operations

Find the remainder:

**Possible Answers:**

-6

**Correct answer:**

When we divide a polynomial by another polynomial we get:

- Quotient
- Remainder (if one exists)

In our problem the long division results in:

- A quotient of
- A remainder of

### Example Question #7 : Polynomial Operations

Divide:

**Possible Answers:**

**Correct answer:**

This can easily be solved by factoring using the difference of cubes formula:

First, convert the given polynomial into a difference of two cubes:

Compare this with the difference of cubes formula above to get:

By dividing the above numerator by the given denominator we get:

### Example Question #8 : Polynomial Operations

Divide:

**Possible Answers:**

**Correct answer:**

Cancel:

### Example Question #9 : Polynomial Operations

Divide:

**Possible Answers:**

**Correct answer:**

Cancel:

### Example Question #10 : Polynomial Operations

Simplify:

**Possible Answers:**

**Correct answer:**

7 in the denominator is a common factor of the three coefficients in the numerator, which allows you to divide out the 7 from the denominator:

Then divide by :