The polynomial function is [tex]x^3+3x^2-18x-40[/tex].
Solution:
Given zeroes are –5, 4, –2.
If a is zero of the polynomial, then (x – a) is factor of the polynomial.
Here the factors of the polynomial are:
(x – (–5)) = x + 5
x – 4 = x – 4
(x – (–2)) = x + 2
On multiplying the factors, we get the polynomial.
[tex](x+5)(x-4)(x+2)=(x^2-4x+5x-20)(x+2)[/tex]
[tex]=(x^2+x-20)(x+2)[/tex]
[tex]=x^3+2x^2+x^2+2x-20x-40[/tex]
[tex]=x^3+3x^2-18x-40[/tex]
[tex](x+5)(x-4)(x+2)=x^3+3x^2-18x-40[/tex]
Hence the polynomial function for given zeroes is [tex]x^3+3x^2-18x-40[/tex].
