Question

Divide the polynomials 4x^4 + 4x - 10 by 2x^2 - 3 to determine the quotient and remainder.

Answer 1

To divide the polynomials 4x^4 + 4x - 10 by 2x^2 - 3, we use long division.

2x^2 + 4
_______________________
2x^2 - 3 | 4x^4 + 0x^3 + 0x^2 + 4x - 10
- (4x^4 - 6x^2)
-----------------
6x^2 + 4x
- (6x^2 - 9)
--------------
13x - 10

So the quotient is 2x^2 + 4 and the remainder is 13x - 10.