Step-by-step explanation:
Given,
The zeros of the polynomial are - 4, - 2, 1 and 4
To find, the polynomial equation = ?
We know that,
The polynomial equation = (x - A)(x - B)(x - C)(x - D)
= (x + 4)(x + 2)(x - 1)(x - 4)
= [(x + 4)(x - 4)] [(x + 2)(x - 1)]
= ([tex]x^{2}-16[/tex])([tex]x^2-x+2x-2[/tex])
= ([tex]x^{2}-16[/tex])([tex]x^2+x-2[/tex])
= [tex]x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32[/tex]
= [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex]
Thus, the required poynomial equation is [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex].
