Higher degree polynomial equations?

a) sum of roots = 8

product and sum of roots = -6 + 18 - 3 = 9

product of roots = - 18

so cubic equation : x^3 - 8x^2 + 9x - 18 = 0

b) I have not done fourth degree polonomials in class, but i can guess....

(x - a)(x - b)(x - c)(x - d) = (x - d)[ x^3 - (a + b + c)x^2 +(ab + ac + bc)x - abc]

=x^4 -(a + b + c + d)x^3 + (ab + ac + bc + d(a +b + c))x^2 - (abc + d(ab + ac + bc))x + abcd

a = 1, b = 2 , c = 3 , d = 5 just substitute.

a)

18 + 9 x - 8 x^2 + x^3

b)

30 - 61 x + 41 x^2 - 11 x^3 + x^4

a) (x-6)(x+1)(x-3) multiply first two, simplify, and then multiply by third term and simplify

b) (x-1)(x-2)(x-3)(x-5) proceed as above, first two, then third, then fourth, for example. Order does not matter, but best to be systematic to avoid errors.