Can someone please help me workout this problem? If the quotient obtained by dividing 8x^4 - 2x^2 + 6x - 7 by 2x+1 is equal to 4x^3 + px^2 - qx +3, then find the remainder and also the values of p and q.

The answer to your question is p = -2 q = -6  remainder = -10

Step-by-step explanation:

Data

Dividend = 8x⁴ - 2x² + 6x - 7

Divisor    = 2x + 1

Quotient = 4x³ + px² - qx + 3

Process

1.- Divide using long division

                                4x³ - 2x² + 3                          

                   2x + 1   8x⁴ + 0x³ - 2x² + 6x - 7

                             - 8x⁴ - 4x³

                                 0   - 4x³ - 2x²

                                      + 4x³ +2x²

                                          0       0   + 6x - 7

                                                          -6x - 3

                                                             0 - 10    Remainder

         px² = -2x²  then  p = -2

         -qx = 6x     then q = -6

3x + 4y -25 =0 represents the amount of change sianna should recieve