dividing a polynomial by a polynomial
example
x-3/x with exponent of 2 -10x+9
or even
2x-3/x with exponent of 2 -10x+9
Thank you any great tutorial sites would help me also.
See
http://www.sosmath.com/algebra/factor/fac01/fac01.html
for how to do these.
To divide a polynomial by a polynomial, you can follow these steps:
1. Make sure both polynomials are written in descending order of exponents.
2. If the divisor (the polynomial you are dividing by) is not in descending order, arrange it accordingly.
3. Perform the polynomial long division. Start by dividing the highest-degree term of the dividend (the polynomial you are dividing) by the highest-degree term of the divisor. This will give you the first term of the quotient.
4. Multiply the divisor by the quotient term you just found and subtract it from the dividend. This will give you the remainder.
5. Bring down the next term of the dividend and repeat the process. Divide it by the highest-degree term of the divisor to find the next term of the quotient. Multiply the divisor by this term and subtract it from the dividend.
6. Continue bringing down the next term of the dividend and repeating the process until you have divided all the terms.
7. The last step is to simplify the quotient if possible. You may need to further divide or factor if necessary.
Now let's apply these steps to the examples you provided:
Example 1: Dividing (x^2 - 10x + 9) by (x - 3)
Step 1: Arrange the dividend in descending order: x^2 - 10x + 9
Step 2: Arrange the divisor in descending order: x - 3
Step 3: Perform polynomial long division:
x - 3 | x^2 - 10x + 9
- (x^2 - 3x)
-------------
-7x + 9
Dividing x^2 by x gives x, which is the first term of the quotient.
Step 4: Multiply (x - 3) by x: (x - 3) * x = x^2 - 3x
Step 5: Subtract (x^2 - 3x) from the dividend: (x^2 - 10x + 9) - (x^2 - 3x) = -7x + 9
Step 6: Bring down the next term (-7x) and repeat the process.
x - 3 | -7x + 9
- (-7x + 21)
------------
-12
Dividing -7x by x gives -7, which is the next term of the quotient.
Step 4: Multiply (x - 3) by -7: (x - 3) * -7 = -7x + 21
Step 5: Subtract (-7x + 21) from the dividend: (-7x + 9) - (-7x + 21) = -12
Since we have no more terms to bring down, we stop here.
Step 7: Simplify the quotient, if necessary. In this case, -12 cannot be simplified further.
Therefore, the quotient is x - 7 and the remainder is -12.
Example 2: Dividing (2x^2 - 10x + 9) by (x - 3)
The steps to solve this example are the same as in Example 1, so I will skip straight to the result.
The quotient is 2x - 4 and the remainder is 21.
As for tutorials and further explanations, here are some helpful websites:
1. Khan Academy: Khan Academy offers comprehensive video tutorials on various math topics, including polynomial division. You can search for "polynomial division Khan Academy" to find their tutorials. (https://www.khanacademy.org/)
2. MathisFun: MathisFun provides explanations and examples for polynomial long division, along with practice questions. You can visit their website and search for "polynomial long division" to access their materials. (https://www.mathsisfun.com/algebra/polynomials-division-long.html)
These resources should provide you with a deeper understanding of polynomial division and help you improve your skills in this topic.