Question

What are the zeros of f left parenthesis x right parenthesis equals x cubed minus 57 x plus 56 ​?

Answer 1

f(x)=x^3-57x+56
Regroup to factor it: f(x)=x^3-x-56x-56=(x^3-x)-(56x+56)
f(x)=x(x^2-1)-56(x+1)
f(x)=x(x+1)(x-1)-56(x+1)
f(x)=(x-1)[x(x+1)-56] =(x-1)(x^2+x-56)=(x-1)(x+8)(x-7)
the zeros are the values of x when f(x)=o
(x-1)(x+8)(x-7)=0
x=1, -8, 7