Answer:
The polynomial of the function degree '4'
x⁴ - x³ -46 x² -80x =0
Explanation:
Explanation:-
Given zeros are 0 ,-5,8,-2
x =0 , x=-5 ,x=8 and x=-2
(x-0) , ( x+5) , (x-8) and (x+2)
The polynomial function with degree '4'
(x-0)(x-(-5)(x-8)(x-(-2) =0
x ( x+5) (x-8) (x+2) =0
(x² +5x)(x-8)(x+2) =0
(x³ -8 x²+5x² -40 x)(x+2) =0
( x³ -3 x² - 40 x) (x +2) =0
x⁴ + 2 x³ - 3 x³- 6 x²-40 x²- 80 x =0
x⁴ - x³ -46 x² -80x =0
Final answer:-
The polynomial of the function degree '4'
x⁴ - x³ -46 x² -80x =0