2x^4-9x#+21x^2-26x+12/2x-3

To simplify the expression (2x^4 - 9x^3 + 21x^2 - 26x + 12) / (2x - 3), we can use polynomial long division.

Step 1: Make sure the polynomial is written in descending order of powers of x.

(2x^4 - 9x^3 + 21x^2 - 26x + 12) / (2x - 3)

Step 2: Divide the highest term of the numerator by the highest term of the denominator to find the first term of the quotient. In this case, divide (2x^4) by (2x). The result is x^3.

x^3
---------------
(2x - 3)

Step 3: Multiply the entire denominator (2x - 3) by the first term of the quotient (x^3). Write the product below the numerator, subtract, and bring down the next term.

x^3 + (3/2)x^2 + (39/4)x + 69/8
_____________________________________
2x - 3 | 2x^4 - 9x^3 + 21x^2 - 26x + 12

2x^4 - 3x^3
__________________
- 6x^3 + 21x^2

- 6x^3 + 9x^2
____________________
12x^2 - 26x

12x^2 - 18x
__________________
- 8x + 12

- 8x + 12
_________________
24

Step 4: Repeat the process until no more terms are left to bring down. The constant term in this case is 24.

Hence, the simplified form of the expression (2x^4 - 9x^3 + 21x^2 - 26x + 12) / (2x - 3) is:

x^3 + (3/2)x^2 + (39/4)x + 69/8 + (24 / (2x - 3))