There's a double zero at 11, so that means (x-11)^2 is a factor
g(-4) = 0 so x+4 = 0 meaning that (x+4) is a factor
g(5) = 0 so x-5 = 0 meaning that (x-5) is a factor
all together, we have
(x-5)*(x+4)*(x-11)^2
let's expand this out
(x-5)*(x+4)*(x-11)^2
(x^2-x-20)*(x^2-22x+121)
x^2(x^2-22x+121) - x(x^2-22x+121) - 20(x^2-22x+121)
x^4-22x^3+121x^2-x^3+22x^2-121x-20x^2+440x-2420
x^4-23x^3+123x^2+319x-2420
This is multiplied by some constant k such that
k*(x^4-23x^3+123x^2+319x-2420) = -6
where plugging in x = 0 leads to -6
Let's plug in x = 0 and find out what happens with k
k*(x^4-23x^3+123x^2+319x-2420)
k*(0^4-23*0^3+123*0^2+319*0-2420)
k*(-2420)
-2420k
So -2420k = -6 leads to k = 3/1210
Therefore, the equation is [tex]y = \frac{3}{1210}(x^4-23x^3+123x^2+319x-2420)[/tex]
