Algebra 1 : Polynomial Operations
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Example Question #1 : How To Divide Polynomials
Simplify
When dividing exponents, you subtract exponents that share the same base, so
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 #1 : Polynomial Operations
Simplify the rational expression.
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 : How To Divide Polynomials
Find the Greatest Common Factor (GCF) of the following polynomial:
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 #3 : How To Divide Polynomials
Divide:
Divide each of the terms in the numerator by the denominator:
Simplify each term above to get the final:
Example Question #2 : Polynomial Operations
Find the quotient:
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 #4 : How To Divide Polynomials
Find the remainder:
-6
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 #3 : How To Divide Polynomials
Divide:
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 #2 : Polynomial Operations
Divide:
Cancel:
Example Question #4 : How To Divide Polynomials
Divide:
Cancel:
Example Question #6 : How To Divide Polynomials
Simplify:
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 
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