Suppose a, b, and c are fixed real numbers such that

b^2 - 4ac ≥ 0. Let r and s be the solutions of

ax^2 + bx + x = 0.

(a) Use the quadratic formula to show that r + s = -b/a and

rs = c/a.

(b) Use part (a) to verify that ax^2 + bx + c =

a(x - r)(x - s).