Form a polynomial whose zeros and degree are given. ​​Zeros: 1​, multiplicity​ 1; -3, multiplicity​ 2; degree 3

Answer 1

For the polynomial p(x) to have a zero at x=1 it should contain the factor (x-1). For it to have a zero at x=-3 with multiplicity 2 it should contain the factor (x-(-3))=(x+3) two times, that is (x+3)^2. Finally, for it to be of degree 3 it should not contain any other factors. Thus we arrive at

p(x) = (x-1) * (x+3)^2 = x^3 + 5 x^2 + 3 x - 9

Of course you can multiply the above polynomial by any nonzero number, the result will be another polynomial satisfying the desired properties.