Which of the following is a polynomial with roots 4, −5, and 7? question 4 options: 1) f(x) = x3 − 6x2 − 27x + 140 2) f(x) = x3 − 6x2 − 20x + 27 3) f(x) = x3 − 20x2 − 27x + 35 4) f(x) = x3 − 20x2 − 35x + 140

If x = 4, then the factor is (x - 4); if x = -5, then the factor is (x + 5); if x = 7, then the factor is (x - 7).  We need to FOIL all these together to get a third degree polynomial.  (x - 4)(x + 5) = (x^2 + x - 20).  Now multiply that by (x- 7):  (x^2+x-20)(x-7) = .  Combine like terms to get  ,  the first choice above.