Question

Consider the polynomial function f(x) = x⁴ + 2x³ + 46x² + 98x - 147. Find the zeros of f(x) and then write f(x) as a product of linear factors.

Answer 1

The zeros of the polynomial function are -3, 1, -7, and 7. The function can be written as a product of linear factors (x + 3)(x - 1)(x + 7)(x - 7).

Step-by-step explanation:

To find the zeros of the polynomial function f(x) = x⁴ + 2x³ + 46x² + 98x - 147, we need to set it equal to zero and solve for x. By factoring or using synthetic division, we find that the zeros are x = -3, x = 1, x = -7, and x = 7.

Next, we can write f(x) as a product of linear factors by using the zeros: f(x) = (x + 3)(x - 1)(x + 7)(x - 7).