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x^2 - x - 6 / x - 3 (dividing polynomials)
- Thread starter fiskonian
- Start date
Were you supposed to use long or synthetic division?
http://www.purplemath.com/modules/polydiv2.htm
Read that and the next page on synthetic division
http://www.purplemath.com/modules/polydiv2.htm
Read that and the next page on synthetic division
im not sure. ill retype the steps in the book for the example problem.
4x^3 - 4x^2 + 5x - 8 / 2x - 1
Step 1: 4x^3 divided by 2x = 2x^2; 2x^2(2x - 1) = 4x^3 - 2x^2
Step 2: Subtract; bring down the next term.
Step 3: -2x^2 divided by 2x = -x; -x(2x - 1) = -2x^2 + x
Step 4: Subtract; bring down the next term.
Step 5: 4x divided by 2x = 2; 2(2x - 1) = 4x - 2
Step 6: Subtract. The remainder is -6. write the remainder as the numerator of a fraction that has 2x - 1 as its denominator. The answer is not a polynomial because of the nonzero remainder.
Hope that helps. i dont understand it at all.
edit - thanks, the purple math helps but i still dont understand this part:
-9x
-----
1x
-----
-10x
if you see what im talking about on that page.
4x^3 - 4x^2 + 5x - 8 / 2x - 1
Step 1: 4x^3 divided by 2x = 2x^2; 2x^2(2x - 1) = 4x^3 - 2x^2
Step 2: Subtract; bring down the next term.
Step 3: -2x^2 divided by 2x = -x; -x(2x - 1) = -2x^2 + x
Step 4: Subtract; bring down the next term.
Step 5: 4x divided by 2x = 2; 2(2x - 1) = 4x - 2
Step 6: Subtract. The remainder is -6. write the remainder as the numerator of a fraction that has 2x - 1 as its denominator. The answer is not a polynomial because of the nonzero remainder.
Hope that helps. i dont understand it at all.
edit - thanks, the purple math helps but i still dont understand this part:
-9x
-----
1x
-----
-10x
if you see what im talking about on that page.
fiskonian said:I don't understand it at all.
OK - I see you are doing polynomial long division - check the link I gave you before:
http://www.purplemath.com/modules/polydiv2.htm
If you don't understand it at all, we unfortunately cannot re-teach material in this environment; you deserve one-on-one attention. I recommend that you go talk with your teacher before or after class and explain that you are not understanding the material.
I wish you the best!
John
fiskonian said:x^2 - x - 6
-------------
x - 3
Okay, I have no idea how to do this.
I read the explanation in my book and it went over my head.
Did you try FACTORING the numerator, and then seeing if you could reduce the resulting fraction?
x^2 - x - 6 can be factored as (x - 3)(x + 2)
So...your division is
(x - 3)(x + 2)
----------------
(x - 3)
Do you see a common factor of (x - 3) in both numerator and denominator? Divide that out ....as long as x is not equal to 3, (x - 3)/(x - 3) = 1.
You'll end up with x + 2.
It is just like reducing (5*3) / 5
If you are trying to kill a fly, a fly-swatter is probably more appropriate than a nuclear bomb.....