Write the polynomial given the real zeros as −1 with multiplicity 1, 1 with multiplicity 2 and 2 with multiplicity 1 and the y-intercept (0, 1).

Answer 1

(x+1)(x-1)^2(x-2) + 3

expand the factors and the constant term is -2, add 3 to get y intercept = 1

take each zero, change its sign and stick an x in front of it. IF it's multiplicity 2, give that factor an exponent of 2. Then multiply them altogether. then add 3

(x^2-2x+1)(x^2-x-2) + 3

multiply it further and you get a 4th degree polynomial

x^4 -3x^3+x^2 +3x -2 + 3

x^4 -3x^3 +x^2 +3x + 1, when x=0, y=1, the y intercept is 1