Final answer:
The difference between functions f(x) and g(x) is h(x), calculated as h(x) = f(x) - g(x). In polynomial form, for h(x) = ax³ + bx² + cx + d, the coefficients are a = 1, b = 4, c = -2, and d = -8.
Step-by-step explanation:
The difference between the two functions f(x) and g(x) is found by subtracting g(x) from f(x). The function h(x) is defined as this difference, i.e., h(x) = f(x) - g(x). Set to the general polynomial form, h(x) = ax³ + bx² + cx + d, we can calculate the coefficients a, b, c, and d for h(x).
Let's discern the coefficients step by step:
f(x) = x³ + 5x² – 1
g(x) = x² + 2x + 7
h(x) = f(x) - g(x) = (x³ + 5x² – 1) - (x² + 2x + 7)
h(x) = x³ + 5x² - x² - 2x - 1 - 7
h(x) = x³ + (5x² - x²) - 2x - (1 + 7)
h(x) = x³ + 4x² - 2x - 8
a = 1
b = 4
c = -2
d = -8