What is the difference of the following polynomials?
(6x^3 - 2x^2 + 4) - (2x^3 + 4x^2 - 5)
A. 4x^3 - 2x^2 -1
B.8x^3 + 6x^2 - 1
C.4x^3 - 2x^2 + 1
D. 4x^3 - 6x^2 + 9
The difference of the polynomials is obtained by subtracting the second polynomial from the first polynomial:
(6x^3 - 2x^2 + 4) - (2x^3 + 4x^2 - 5)
Distributing the negative sign to the second polynomial:
= 6x^3 - 2x^2 + 4 - 2x^3 - 4x^2 + 5
Combining like terms:
= (6x^3 - 2x^3) + (-2x^2 - 4x^2) + (4 + 5)
= 4x^3 - 6x^2 + 9
Therefore, the difference of the polynomials is 4x^3 - 6x^2 + 9.
The correct answer is D.