Answer:
The function [tex]f(x)=x^3+\mathbf{1}x^2-\mathbf{17}x+\mathbf{15}[/tex]
Step-by-step explanation:
We have the polynomial having zeros 1,3,-5
We can write them as:
x=1,x=3,x=-5
or
x-1=0, x-3=0,x+5=0
Multiplying all terms:
[tex](x-1)(x-3)(x+5)\\=(x(x-3)-1(x-3))(x+5)\\=(x^2-3x-1x+3)(x+5)\\=(x^2-4x+3)(x+5)\\=(x^2-4x+3)+5(x^2-4x+3)\\=^3-4x^2+3x+5x^2-20x+15\\=x^3-4x^2+5x^2+3x-20x+15\\=x^3+x^2-17x+15[/tex]
So, The function [tex]f(x)=x^3+\mathbf{1}x^2-\mathbf{17}x+\mathbf{15}[/tex]
