Answer:
x^3 + 6x^2 - 9x - 14
Explanation:
The zeros of a polynomial are the solutions to its factors. When the factors are set equal to 0, the zeros are the result. To write the equation, use the zeros to reverse the process to find the factors which multiply to make the equation.
x = -1 results from the factor x + 1 = 0
x = 2 results from the factor x - 2 = 0
x = 7 results from the factor x - 7 = 0
Since all zeros have multiplicity of 1, this means there is no exponent on the factored expressions. So the equation of the polynomial is (x+1)(x-2)(x-7).
Multiply the factors using the distributive property to find the equation in standard form.
(x+1)(x-2)(x-7)
(x^2 + 1x -2x - 2)(x+7)
(x^2 - x - 2)(x+7)
x^3 - x^2 - 2x + 7x^2 - 7x - 14
x^3 + 6x^2 - 9x - 14