Question

Given the functions f(x) = (x² + 7x - 12) and g(x) = (x² - 9x + 1), determine the values of a, b, c, d, and e in the equation f(x) • g(x) = ax⁴ - bx³ - cx² + dx - e.

a. a = 1, b = -2, c = -23, d = -26, e = 12
b. a = 1, b = 16, c = 10, d = 0, e = -12
c. a = 1, b = -16, c = -10, d = 0, e = 12
d. a = 1, b = 2, c = 23, d = 26, e = -12

Answer 1

The values of a, b, c, d, and e can be determined by multiplying the given functions together and comparing with the equation provided.

The correct values are a = 1, b = 2, c = 23, d = 26, e = -12.

Step-by-step explanation:

In this case, the values of a, b, c, d, and e are given in the options as a = 1, b = -2, c = -23, d = -26, and e = 12. The equation f(x) • g(x) can be expanded as (x² + 7x - 12) • (x² - 9x + 1). Multiplying these expressions together results in a fourth-degree polynomial. By multiplying and combining like terms, we can find the coefficients of the polynomial equation.

Let's multiply the polynomials: (x² + 7x - 12) • (x² - 9x + 1).

We get ax⁴ - bx³ - cx² + dx - e = x⁴ - 2x³ - 23x² + 26x - 12. Comparing this with the given equation, we can see that a = 1, b = -2, c = -23, d = 26, and e = -12. Therefore, the correct answer is option D: a = 1, b = 2, c = 23, d = 26, e = -12.