Question 1. (a) Suppose that a cubic polynomial x3 + Ax2 + Bx + C factors into (x a)(x b)(x c) where x is a variable and a, b, c are real numbers.

Question 1.

(a) Suppose that a cubic polynomial x3 + Ax2 + Bx + C factors into (x − a)(x − b)(x − c) where x is a variable and a, b, c are real numbers. Calculate the ex- pressions of A, B, C in terms of a, b, c.

A=

B=

C=

(b) Find all the roots of f(x) = x3 − 4x2 − 11x + 30.