Perform the indicated process on the polynomials:

4x^3 - 7x - 6 / 2x - 3

To perform the indicated process of dividing the polynomial (4x^3 - 7x - 6) by (2x - 3), we can use the long division method. The goal is to divide the highest degree term of the dividend (4x^3) by the highest degree term of the divisor (2x) and obtain the quotient.

1. First, write the dividend (4x^3 - 7x - 6) inside the long division symbol (÷) and the divisor (2x - 3) to the left of it.
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2x - 3 │ 4x^3 - 7x - 6

2. Determine what term must be multiplied by the divisor (2x - 3) to obtain the first term of the dividend (4x^3). In this case, multiplying (2x - 3) by (2x^2) will give us (4x^3).
_____
2x - 3 │ 4x^3 - 7x - 6
-(4x^3 - 6x^2)
______
-x^2

3. Subtract the result obtained in step 2 from the first two terms of the dividend and write the result below the line.
_____
2x - 3 │ 4x^3 - 7x - 6
-(4x^3 - 6x^2)
______
-x^2 - 7x

4. Bring down the next term from the dividend (-6x) and place it after the result obtained in the previous step (-x^2 - 7x).
_____
2x - 3 │ 4x^3 - 7x - 6
-(4x^3 - 6x^2)
______
-x^2 - 7x - 6x

5. Determine what term must be multiplied by the divisor (2x - 3) to obtain the next term in the dividend (-x^2 - 7x). In this case, multiplying (2x - 3) by (-1/2) will give us (-x^2 + (3/2)x).
_____
2x - 3 │ 4x^3 - 7x - 6
-(4x^3 - 6x^2)
______
-x^2 - 7x - 6x
+ (x^2 - (3/2)x)
______
- (13/2)x - 6x

6. Subtract the result obtained in step 5 from the previous result (- (13/2)x - 6x) and write the result below the line.
_____
2x - 3 │ 4x^3 - 7x - 6
-(4x^3 - 6x^2)
______
-x^2 - 7x - 6x
+ (x^2 - (3/2)x)
______
- (13/2)x - 6x - 6
- ((- (13/2)x - 6x))
______
0

7. Since the degree of the result (- (13/2)x - 6x - 6) is less than the degree of the divisor (2x - 3), the division process is complete.

Therefore, the quotient is - (13/2)x - 6x - 6.