Question 839332
"Write an equation of a quintic polynomial with roots 1, -2, 3, and i (imaginary, not a variable) with a y-intercept of 18"
:
The factors derived from the above: (x-1)(x+2)(x-3)(x^2+1)
FOIL (x-1)(x+2) = x^2 + x - 2
then
(x-3)*(x^2 + x - 2) = x^3 - 2x^2 - 5x + 6 
then
(x^2+1)*(x^3-2x^2-5x+6) = x^5 - 2x^4 - 4x^3 + 4x^2 - 5x + 6
To get a y intercept of 18 multiply eq by 3
3x^5 - 6x^4 - 12x^3 + 12x^2 - 15x + 18 is polynomial
:
Looks like this
{{{ graph( 300, 200, -6, 6, -80, 60, 3x^5 - 6x^4 - 12x^3 + 12x^2 - 15x + 18)}}}