Question 133276
If a polynomial has n zeros, it must be of degree n. (Fundamental Theorem of Algebra).  Also, if a is a zero of a polynomial equation, then {{{x-a}}} must be a factor of the polynomial.


So, for problem 18, you have three zeros, so you must have three binomial factors that will expand to a 3rd degree polynomial.


{{{(x-1)(x-(-3))(x-4)=(x-1)(x+3)(x-4)=(x^2+2x-3)(x-4)=x^3+2x^2-3x-4x^2-8x+12=x^3-2x^2-11x+12}}}


Do the other problem the same way, except that you have 4 zeros, so you will have 4 factors and a 4th degree polynomial at the end.