Equation in factored form is g(x) = (x-8)(x-7/2)(x+5/3) .
The given zeroes are of a cubic polynomial .
A cubic polynomial is a polynomial of degree 3. There are several methods to solve a cubic equation but we will do this by factorisation method.
a[tex]x^{3}[/tex] + b[tex]x^{2}[/tex] + cx + d = 0, a ≠ 0
Sum of zeroes = S = 8 + 7/2 - 5/3
= 59/6
Product of zeroes = P = 8*(7/2)*[(-5)/3]
= -140/3
Evaluating the sum t of the product of zeroes taken two at a time:
T = 8*(7/2) + 8*(-5/3) + (7/2)*(-5/3)
= 44/5
S = -b/a
P = c/a
T = -d/a
g(x) = k*([tex]x^{3}[/tex] - S[tex]x^{2}[/tex] + Tx - P) = 0
Substituting values of S, T and P in the equation we get ,
= K([tex]x^{3}[/tex] - 59/6[tex]x^{2}[/tex] + 44/5x +140/3)
= (x-8)(x-7/2)(x+5/3)
To learn more on cubic polynomial follow the below link :
https://brainly.com/question/4098038
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