Suppose a, b, c are fixed real numbers such that b2 − 4ac ≥ 0. Let r and s be the solutions of
ax2 + bx + c = 0.
(a) Use the quadratic formula to show that r + s = −b/a and rs = c/a.
(b) Use part (a) to verify that ax2 + bx + c = a(x − r)(x − s).
(c) Use part (b) to factor x2 − 2x − 1 and 5x2 + 8x + 2.
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