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.

Sure, I can help you with that! Long division is a method used to divide polynomials. In this case, you want to divide x^4 by (x-1)(x^2+1).

To perform long division, follow these steps:

Step 1: Write the dividend (x^4) inside the long division symbol (⌒) and the divisor ((x-1)(x^2+1)) outside the long division symbol.

__________
(x-1)(x^2+1) | x^4

Step 2: Divide the first term in the dividend (x^4) by the first term in the divisor (x). Place the result (x^3) above the line.

__________
(x-1)(x^2+1) | x^4
x^3

Step 3: Multiply the divisor (x-1)(x^2+1) by the result (x^3) and write the product below the dividend.

__________
(x-1)(x^2+1) | x^4
x^3
____________
x^3(x-1)(x^2+1)

Step 4: Subtract the product from the dividend. Write the result below the line.

__________
(x-1)(x^2+1) | x^4
x^3
____________
x^3(x-1)(x^2+1)
- (x^3(x^2+1))

Step 5: Bring down the next term from the dividend. In this case, it is 0x^2.

__________
(x-1)(x^2+1) | x^4
x^3
____________
x^3(x-1)(x^2+1)
- (x^3(x^2+1))
____________
0x^2

Step 6: Repeat steps 2 to 5 until you have no more terms to bring down or the degree of the remaining term is less than the degree of the divisor.

At this point, there are no more terms to bring down, and the degree of the remaining term (0) is less than the degree of the divisor. Therefore, the long division is complete.

The quotient is x^3, and there is no remainder. So, the result of x^4 divided by (x-1)(x^2+1) is x^3.