Question

a polynomial f(x) is divisible by x - k without a remainder. this means: a. k is a coefficient of f(x) b. f(x) is undefined at x = k c. f(k) equals zero d. x - k is a factor of f(x)

Explanation:

According to the factor - theorem in algebra, if a polynomial \(f(x)\) is divisible by \(x - k\) without a remainder, then \(x - k\) is a factor of \(f(x)\) and \(f(k)=0\). Option a is incorrect as \(k\) is not a coefficient. Option b is wrong since polynomials are defined for all real numbers.

Answer:

C. \(f(k)\) equals zero, D. \(x - k\) is a factor of \(f(x)\)