Question

Help please

If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)?

Answer 1

Explanation:

To find (f/g)(x), we need to divide f(x) by g(x).

(f/g)(x) = f(x) / g(x)

Substituting the given expressions for f(x) and g(x):

(f/g)(x) = (x^4 - x^3 + x^2) / (-x^2)

Now we can simplify by dividing the terms individually:

(f/g)(x) = x^4 / -x^2 - x^3 / -x^2 + x^2 / -x^2

(f/g)(x) = -x^2 - (-x) + 1

(f/g)(x) = -x^2 + x + 1

So, (f/g)(x) = -x^2 + x + 1