### All Algebra 1 Resources

## Example Questions

### Example Question #5 : How To Divide Polynomials

Divide:

**Possible Answers:**

**Correct answer:**

Cancel:

### Example Question #6 : How To Divide Polynomials

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 :

### Example Question #11 : Polynomial Operations

Simplify:

**Possible Answers:**

**Correct answer:**

Use the properties of powers:

We can cancel now:

### Example Question #12 : Polynomial Operations

**Possible Answers:**

**Correct answer:**

To easily divide the polynomials, factor the numerator to get

Then, you can cancel out since it is present in both the numerator and the denominator, leaving you with just .

### Example Question #13 : Polynomial Operations

**Possible Answers:**

**Correct answer:**

First, factor the numerator to get

Since is in both the numerator and the denominator, they cancel each other out. This leaves just as the simplified version of the expression.

### Example Question #71 : Polynomials

Simplify this expression to its lowest terms:

**Possible Answers:**

**Correct answer:**

When we divide a complex set of variables which are all being multiplied by another similar set of variables which are being multiplied (as in our problem!) we are able to handle each separate variable as it's own division problem. So, that the complex fraction

is really 4 separate fractions:

And, when we divide like terms with exponents, we subtract the powers! So, we are able to eliminate the , we leave one in the denominator and one in the numerator! is 5, so we leave the 5 in the numerator as well. This leaves us with the answer:

### Example Question #15 : Polynomial Operations

Simplify the fraction to its simplest terms:

**Possible Answers:**

**Correct answer:**

When we divide a complex set of variables which are all being multiplied, by another similar set of variables which are being multiplied (as in our problem!) we are able to handle each separate variable as it's own division problem. So the complex fraction:

is really 4 separate fractions:

And, when we divide like terms with exponents, we subtract the powers! So, we are able to do this and we leave , & in the denominator and, since there is nothing left in the numerator we put the placeholder, 1, there!

so we leave the 1 in the numerator and put the 2 as the coefficient in the denominator. Leaving us with the answer:

### Example Question #1 : Simplifying Polynomials

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 #72 : Polynomials

Simplify the following:

**Possible Answers:**

This fraction cannot be simplified.

**Correct answer:**

First we will factor the numerator:

Then factor the denominator:

We can re-write the original fraction with these factors and then cancel an (x-5) term from both parts:

### Example Question #1 : Operations With Polynomials

Divide by .

**Possible Answers:**

**Correct answer:**

First, set up the division as the following:

Look at the leading term in the divisor and in the dividend. Divide by gives ; therefore, put on the top:

Then take that and multiply it by the divisor, , to get . Place that under the division sign:

Subtract the dividend by that same and place the result at the bottom. The new result is , which is the new dividend.

Now, is the new leading term of the dividend. Dividing by gives 5. Therefore, put 5 on top:

Multiply that 5 by the divisor and place the result, , at the bottom:

Perform the usual subtraction:

Therefore the answer is with a remainder of , or .

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