Plz cud sombdy show me long division method of x^4/(x-1)(x^2+1)???? Plz note (x-1)(x^2+1) is in the denominator.
Why not take the extra few seconds and post using proper English ?
I expanded the denominator to get
x^3 - x^2 + x - 1 and I then divided x^4 by that
It is hard to show the actual long division here, I assume you know how to do that.
I got
x+1 with a remainder of 1
so x^4/((x-1)(x^2+1)) = (x+1) + 1/((x-1)(x^2+1))
visit calc101.com and click on the long division link. It will show all the intermediate steps in the division.
Sure! I'd be happy to explain the long division method for dividing a polynomial by another polynomial. In this case, you want to divide the polynomial x^4 by the polynomial (x-1)(x^2+1).
Step 1: Write the dividend (x^4) inside the long division symbol (÷).
___________________________________
(x-1)(x^2+1) | x^4
Step 2: Divide the highest degree term of the dividend (x^4) by the highest degree term of the divisor (x^2). This will give you the quotient term for that position. Write this term above the long division symbol.
x^2
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(x-1)(x^2+1) | x^4
x^2
Step 3: Multiply the entire divisor (x-1)(x^2+1) by the quotient term you just found (x^2), and write the result underneath the dividend term from step 2.
x^2
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(x-1)(x^2+1) | x^4
- x^4 + x^2
Step 4: Subtract the expression obtained in step 3 from the dividend. Write the result below the line.
x^2
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(x-1)(x^2+1) | x^4
- x^4 + x^2
___________________
0 - x^2
Step 5: Bring down the next term from the dividend (0 - x^2) and place it after the difference obtained in the previous step.
x^2
___________________________________
(x-1)(x^2+1) | x^4
- x^4 + x^2
___________________
0 + (-x^2)
Step 6: Repeat steps 2 to 5 until you have exhausted all the terms of the dividend.
x^2 - 1
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(x-1)(x^2+1) | x^4
- x^4 + x^2
___________________
0 + (-x^2) + 1
Step 7: Write the final result with the quotient and remainder.
x^4 / [(x-1)(x^2+1)] = x^2 - 1 / [(x-1)(x^2+1)] + 1 / [(x-1)(x^2+1)]
So, the long division of x^4 by (x-1)(x^2+1) results in the quotient x^2 - 1 and a remainder of 1 / [(x-1)(x^2+1)].
I hope this helps! Let me know if you have any more questions.