Question

What information in the problem is necessary to rewrite f(x) as a product of linear factors using long division?

a) Coefficients of f(x)
b) Degree of f(x)
c) Zeros of f(x)
d) Leading coefficient of f(x)

Answer 1

To rewrite f(x) as a product of linear factors using long division, you need to know the zeros of f(x). The coefficients, degree, and leading coefficient of f(x) are also important for determining the linear factors.

Step-by-step explanation:

To rewrite f(x) as a product of linear factors using long division, the necessary information from the problem is the zeros of f(x). These zeros correspond to the linear factors that will divide f(x) evenly. By dividing f(x) by (x - zero), we can obtain the linear factors.

The coefficients of f(x) determine the values of the constants in the linear factors, while the degree of f(x) helps determine the number of linear factors. The leading coefficient of f(x) is important in determining the sign of the linear factors.