### All Algebra 1 Resources

## Example Questions

### Example Question #18 : Simplifying Expressions

Simplify the expression:

**Possible Answers:**

The fraction cannot be simplified further.

**Correct answer:**

When dividing polynomials, subtract the exponent of the variable in the numberator by the exponent of the same variable in the denominator.

If the power is negative, move the variable to the denominator instead.

First move the negative power in the numerator to the denominator:

Then subtract the powers of the like variables:

### Example Question #19 : Polynomial Operations

Simplify:

**Possible Answers:**

**Correct answer:**

The numerator is equivalent to

The denominator is equivalent to

Dividing the numerator by the denominator, one gets

### Example Question #4 : Adding And Subtracting Rational Expressions

Subtract:

**Possible Answers:**

**Correct answer:**

First let us find a common denominator as follows:

Now we can subtract the numerators which gives us :

So the final answer is

### Example Question #64 : Solving Rational Expressions

Simplify:

**Possible Answers:**

None of the above

**Correct answer:**

Factor both the numerator and the denominator which gives us the following:

After cancelling we get

### Example Question #3 : Multiplication And Division

Simplify the following:

**Possible Answers:**

**Correct answer:**

We are dividing the polynomial by a monomial. In essence, we are dividing each term of the polynomial by the monomial. First I like to re-write this expression as a fraction. So,

So now we see the three terms to be divided on top. We will divide each term by the monomial on the bottom. To show this better, we can rewrite the equation.

Now we must remember the rule for dividing variable exponents. The rule is So, we can use this rule and apply it to our expression above. Then,

### Example Question #2 : 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 #21 : Simplifying Polynomials

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 #82 : Variables

Divide the polynomials:

**Possible Answers:**

**Correct answer:**

In order to divide these polynomials, we will need to factorize both the top and the bottom expressions.

Cancel out the common terms in the numerator and denominator.

The answer is:

### Example Question #83 : Variables

Divide the polynomials and .

**Possible Answers:**

**Correct answer:**

Write an expression to divide the polynomials.

Both polynomials can be factorized.

The numerator will be simplified to .

The denominator cannot be factorized as is. Pull a common factor of two in the denominator.

The term can be factorized to .

We can now rewrite the fraction.

The common terms in the numerator and denominator can be cancelled.

Distribute the two in the denominator through both terms in the binomial.

The answer is:

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

Expand:

**Possible Answers:**

**Correct answer:**

Distribute through every term in the parentheses.

This gives us the following:

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