Question 122093
Write the polynomials having the following zeros:
1) -1, 1, 6
If the polynomial has these zeros, then you can write:
x = -1, so x+1 = 0
x = 1, so x-1 = 0
x = 6, so x-6 = 0
 This means that:
{{{(x+1)(x-1)(x-6) = 0}}} Multiply these factors using FOIL to get the generating polynomial:
{{{(x+1)(x-1)(x-6) = (x^2-1)(x-6)}}}={{{x^3-6x^2-x+6}}} This is the polynomial.
Using the same technique:
2) 2, -2, -3
If the polynomial has these zeros, then you can write:
x = 2, so x-2 = 0
x = -2, so x+2 = 0
x = -3, so x+3 = 0
This means that:
{{{(x-2)(x+2)(x+3) = 0}}} Multiply these factors using FOIL to get the generating polynomial:
{{{(x-2)(x+2)(x+3) = (x^2-4)(x+3)}}}={{{x^3+3x^2-4x-12}}} This is the polynomial.
Do get the idea?