Question

Find a polynomial function of degree 3 that satisfies the given conditions:

Zeros of -3, -4, and 1, and f(-1) = 12.

A) f(x) = -3(x + 3)(x + 4)(x - 1)
B) f(x) = (x + 3)(x + 4)(x - 1) + 12
C) f(x) = 12(x + 3)(x + 4)(x - 1)
D) f(x) = (x + 3)(x + 4)(x - 1) - 12

Answer 1

To find a polynomial function of degree 3 with given zeros and a specific value, we can use the factor theorem. In this case, the correct polynomial function that satisfies the given conditions is f(x) = -3(x + 3)(x + 4)(x - 1).

Step-by-step explanation:

To find a polynomial function of degree 3 with zeros -3, -4, and 1, we can use the factor theorem. The factor theorem states that if a polynomial has a zero at a certain number, then (x - the zero) is a factor of the polynomial. So, our polynomial function will be of the form f(x) = a(x + 3)(x + 4)(x - 1). To find the value of 'a', we can use the given condition f(-1) = 12. Substituting -1 for x in our function, we get 12 = a(-1 + 3)(-1 + 4)(-1 - 1), which simplifies to 12 = a(2)(3)(-2). Solving for 'a', we get a = -3. Hence, the correct polynomial function that satisfies the given conditions is f(x) = -3(x + 3)(x + 4)(x - 1).