Let f(x)=-16x^2-x^3 and g(x)=-2-4x^2. Then f(x)-g(x) equals____?
A. 1-2x^2-x^3
B. -1-2x^2+x^3
C. 1+2x^2-x^3
D. -1+2x^2+x^3
To find the expression for f(x) - g(x), we simply subtract the two functions term by term.
Given:
f(x) = -16x^2 - x^3
g(x) = -2 - 4x^2
To find f(x) - g(x), we subtract the corresponding coefficients of each term:
f(x) - g(x) = (-16x^2 - x^3) - (-2 - 4x^2)
When we subtract a negative number, it is the same as adding the positive number:
f(x) - g(x) = -16x^2 - x^3 + 2 + 4x^2
Now, we group the like terms together by combining the coefficients of x^2 and x^3 separately:
f(x) - g(x) = (-16x^2 + 4x^2) + (-x^3) + 2
Simplifying further:
f(x) - g(x) = -12x^2 - x^3 + 2
Therefore, the expression for f(x) - g(x) is -12x^2 - x^3 + 2.
None of the answer choices given match this expression, so none of the options A, B, C, or D are correct.