Question

Assume f(w)=-w2 - 4w - 1 and g(w)=2w2 + 5w - 2, find f(w) - g(w).

Answer 1

To find f(w) - g(w), you subtract the polynomial g(w) from f(w), combine like terms, and simplify to get the result -3w^2 - 9w + 1.

Step-by-step explanation:

To find f(w) - g(w), we subtract the function g(w) from the function f(w). We are given that f(w)=-w2 - 4w - 1 and g(w)=2w2 + 5w - 2. So we perform the subtraction:

f(w) - g(w) = (-w2 - 4w - 1) - (2w2 + 5w -2)

Now, distribute the negative sign through the expression g(w) and combine like terms:

f(w) - g(w) = -w2 - 4w - 1 - 2w2 - 5w + 2

Combine like terms:

f(w) - g(w) = -w2 - 2w2 - 4w - 5w - 1 + 2f(w) - g(w) = -3w2 - 9w + 1

Therefore, the result of f(w) - g(w) is -3w2 - 9w + 1.