What is the difference of the following polynomials? %C2%A0%C2%A0 (6x3 – 2x2 + 4) – (2x3 + 4x2 – 5) ______________ (1 point) Responses 4x3 – 2x2 – 1 4 x 3 – 2 x 2 – 1 8x3 + 6x2 – 1 8 x 3 + 6 x 2 – 1 4x3 – 2x2 + 1 4 x 3 – 2 x 2 + 1 4x3 – 6x2 + 9
To find the difference of the two polynomials, we subtract the second polynomial from the first polynomial:
(6x^3 – 2x^2 + 4) - (2x^3 + 4x^2 - 5)
Subtracting like terms, we get:
6x^3 - 2x^2 + 4 - 2x^3 - 4x^2 + 5
Combining like terms, we have:
(6x^3 - 2x^3) + (-2x^2 - 4x^2) + (4 + 5)
4x^3 - 6x^2 + 9
Therefore, the difference of the two polynomials is 4x^3 - 6x^2 + 9.