Answer:
f(x) = 2x³ - 12x² - 2x + 60
Step-by-step explanation:
Given that the zeros are x = - 2, x = 3, x = 5 , then the factors are
(x + 2), (x - 3), (x - 5)
The polynomial is then the product of the factors, that is
f(x) = a(x + 2)(x - 3)(x - 5) ← a is a multiplier
To find a substitute (6, 48) into the polynomial
48 = a(8)(3)(1) = 24a ( divide both sides by 24 )
a = 2 , thus
f(x) = 2(x + 2)(x - 3)(x - 5) ← expand the last 2 factors using FOIL
= 2(x + 2)(x² - 8x + 15) ← distribute the parenthesis
= 2(x³ - 8x² + 15x + 2x² - 16x + 30)
= 2(x³ - 6x² - x + 30) ← distribute by 2
= 2x³ - 12x² - 2x + 60
, you have
is odd, i.e. 
, you have
