Question

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.

Answer 1

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

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