1) Suppose that f is a polynomial function and c is a number. If you divide f(x) by x − c, then what will the remainder be?

2) Suppose that f is a polynomial function with rational coefficients and c is an integer. If x − c is a factor of f(x), then what is f(c)?

3) Suppose that f is a polynomial function with real coefficients, a and b are real numbers with b ≠ 0, and the complex number a + bi is a root (aka zero) of f.

a) What other complex number must be a root of f?

b) What polynomial in x (with real coefficients) must be a factor of f(x)?